The question implicitly assumed many things that are not true. Hong Kong is very different from the UK and thus it is hard to provide a good comparison. Even if we use London for a more like-for-like comparison, the two cities' outgoing expenditure composition is very different from each other, with London featuring more expensive non-rent bills. This leads to the unfortunate conclusion from the OP that "people from the UK have much cash to spare due to lower rent and higher income".
The energy crisis disproportionately affects those with lower income, many of which live in social/public housing. On that front, those in Hong Kong are much better looked after than those in London / the UK financial-wise, with the former's rent taking a much lower percentage of their income. Nonetheless, a rapidly surging expenditure will still be harmful to many regardless of where they live due to its unpredictable nature. This is in contrast to a consistently high expenditure (e.g. high rent in Hong Kong) which people can plan around.
And who said people are coping in Hong Kong? Complaints are just as rife - they are just not in the language/outlets that the OP is familiar with :)
Why is Britain crippled by bills of several hundred pounds per month while Hong Kongers can cope with rents that are much much more expensive (£1000/month more expensive, if not more)?
This question is perhaps ill-formed, likely due to some implicit assumptions that turn out to be not true. This answer attempts to call out a few of the said assumptions.
1. Hong Kong is very different from the UK (in an urban development sense).
As other answers have pointed out, Hong Kong is highly urbanised, while many places in the UK remain rural. This has implications on the efficiency of and hence the cost of running different infrastructures, be it energy, transport or information.
It will be much fairer to compare the bills/rent in Hong Kong to a similarly urbanised area in the UK. Greater London (London hereafter) is a good candidate. At a stretch, one might consider Greater Manchester, West Midlands, or West Yorkshire.
The rest of the answer will use numbers specific to London. The statistics quoted by the OP for London are as follows:
- Median one-bedroom flat rent: £1250 , as compared to ~HK$15500 = £1630 in HK [2,3].
- Hourly minimum wage: £9.50 / £11.05 (London living wage ), as compared to $37.5 = £4 in HK.
- Median monthly pay (all employees): £2647 (£31,766 pa ), as compared to HK$18,700 pm = £1968.
2. The outgoing expenditure composition for a Londoner (as someone who is perhaps more comparable) and a Hong Konger are very different.
It is certainly a pitfall to assume the composition of one's outgoing expenditure (i.e. the percentage of income that gets taxed, or that goes to rent, bills, food & drinks, etc.) is similar in different places. They are not. In fact, there are wild differences between London and Hong Kong:
- Income Tax: Assuming the person has stable income over the year and they file their taxes separately, in the tax year 2021/22 the median pay person in London is expected to pay £542 in income tax and national insurance contributions . The median pay person in Hong Kong is expected to pay zero in salaries tax . In fact, with the 100% tax reduction up to HK$10,000 which has been in effect for a few years, the person in Hong Kong will only pay their first HKD of salaries tax when their monthly income is over HK$24,095.
One might notice after income tax and NI contributions, the take-home pay for a median pay Londoner (£2105) is not that much different from a median pay Hong Konger (£1968).
Council Tax: A typical London one-bedroom property will fall in Bands A-C for Council Tax, which sets a household back by £90-£120 per month (pm) . In Hong Kong, there is a similar bill known as rates. This sets a household occupying an average one-bedroom property back by HK$360 = £38 pm .
Energy: A typical UK two-person, one-bedroom household consumes 1800 kWh of electricity and 8000 kWh of gas per year, with London using marginally less . In Aug 2022, a London household is expected to pay £115 pm under the April 2022 price cap . On the other hand, an average Hong Kong two-person household consumes 3200 kWh of electricity and 1350 kWh (4860 MJ) of town gas/LPG . The household is expected to pay HK$500 = £52.5 pm in energy bills [13-15].
Water: A typical UK two-person household consumes 285L of water per day . In Aug 2022 Thames Water will charge the household £29 per month for water and wastewater services . An average Hong Kong two-person household consumes 260L of water per day . They will get charged HK$35 = £3.65 pm for the same service .
Broadband: A 50Mb+ broadband service in London (e.g. BT, EE, and many others) generally costs ~£20-£30 pm . A 100Mb+ broadband service in Hong Kong generally costs ~HK$108-228 = £11-24 pm .
This means it will cost a London two-person household ~£1525 and a Hong Kong two-person household ~£1740 to rent and maintain a one-bedroom property in their respective location. It still costs more to rent in Hong Kong, but certainly not as much as £1000+ pm as alluded by the OP.
One might argue that will still leave an average Londoner with an extra £245 (including a £137 extra take-home pay and 215 / 2 = £108 savings in rent and bills) as compared to an average Hong Konger, which is not an insignificant sum. It is important to remember that different aspects of life cost differently in different parts of the world. While fresh groceries are cheaper in London as compared to Hong Kong, it is much more expensive in London to commute via public transport, to eat out, or generally to get any kind of services from others (childcare, cleaning, just to name a few). That extra money buffer will disappear in no time.
3. The distribution of rent charged is different between Hong Kong and London (and the UK), with the least well-off in Hong Kong in a better place than those in London or the UK.
Another pitfall when dealing with this topic is to observe the median rent (for private rental) in Hong Kong is higher than that in London, and then attempt to generalise to all other rental sectors. As we will show below, this is not the case.
The original question was likely asked against the backdrop of surging energy prices in the UK. It disproportionately affects the least well-off in society, who are likely to live in social/public housing.
In Hong Kong, 30.4% of Hong Kong households live in public rented housing , paying a monthly rent of HK$2272 = £240 on average. There is also a law that caps the rent-to-income ratio across all these renters to 10% . In contrast, 22% of London households live in social housing, paying an average monthly rent of £559. These people are facing a rent-to-income ratio of 30% on average. The corresponding numbers for the UK are 17%, £442, and 27% .
In other words, the least well-off in Hong Kong are better looked after than their London/UK counterparts financial-wise. With their rent taking a smaller part of their income, the said group in Hong Kong stands a higher chance to be able to absorb any shock in increasing bills than their London/UK counterparts.
4. A consistently high expenditure is different from a rapidly surging expenditure, with the latter more apparent in the UK than in Hong Kong.
The OP, in their question, may have conflated a recent event ("Britain crippled by bills of several hundred pounds") with a long-term phenomenon ("Hong Kongers cope with rents that are much more expensive").
The latter is a relatively benign problem (see the section below). Real estate in Hong Kong has been consistently expensive for decades. As long as its price stays consistent (both in absolute value and growth rate), the market will factor that into any cost of living and hence compensation calculations. Society will also adapt its behaviour around the fact that real estate is expensive.
The former is a much bigger problem. While it is in no way as bad as recent hyperinflation events in other nations, an unforeseen jump in inflation means households which planned a couple hundred pounds buffer will see it suddenly go poof, and households that used to just manage are now a couple hundred pounds in debt. It is not the amount, but the unpredictability of events and cash flow that is harmful.
To put the degree of change (and hence uncertainty) in perspective, inflation (year-on-year increase in CPI) in the UK increased from ~3% in Aug 2021 to ~10% in Aug 2022 , while the same number in Hong Kong is still holding at a healthy 1-2% around the same period . The headline energy price cap in the UK was set to increase by 80% by Oct 2022  before the Government intervenes, which brings the increase to a more manageable 26.8% . Meanwhile, the average increase in electricity tariff in Hong Kong during a similar period is 7.6%-13.5% [29,30].
5. People complain about rising living costs nonetheless.
The OP postulates that people in Hong Kong are coping, which is unlikely to be true. Complaints about the hostile housing market for first-time buyers and MTR (which runs the metro in Hong Kong) increasing their fares again are rife. News on surging electricity costs and Fed rate hikes are also making the rounds, creating many who are a bit touchy.
Such complaints are likely not reaching the OP because:
- They are covered by outlets that the OP does not frequent, and
- They are not in a language that the OP is familiar with.
Long list of references and calculations:
 Office for National Statistics, UK. Private rental market in London: July 2021 to June 2022. Available: https://www.ons.gov.uk/peoplepopulationandcommunity/leisureandtourism/adhocs/15003privaterentalmarketinlondonjuly2021tojune2022
 Census and Statistics Department, Government of Hong Kong SAR. Hong Kong
Monthly Digest of Statistics, Section 8 Housing and Property. Available: https://www.censtatd.gov.hk/en/data/stat_report/product/B1010082/att/B10100822022MM09B0100.pdf.
HK$15500 figure estimated from HK$389 (Table 8.12, Row 2022/07, Column Less than 40 sq. m. - Kowloon) multiplied by 40 sq. m.
 Exchange rate at 11 Aug 2022 (when the question is asked) was £1 = ~HK$9.5 according to xe.com.
 Greater London Authority. London Living Wage. Available: https://www.london.gov.uk/what-we-do/business-and-economy/london-living-wage
 Office of National Statistics, UK. Earnings and hours worked, place of residence by local authority: ASHE Table 8 (2021 Edition). Available: https://www.ons.gov.uk/employmentandlabourmarket/peopleinwork/earningsandworkinghours/datasets/placeofresidencebylocalauthorityashetable8. Table 8.7a.
 Income tax - Taxable income: 31766 - 12570 (personal allowance) = £19,196; Income tax payable: 19196 * 20% = £3839.2 pa.
National insurance - Income above primary threshold: 31766 - 9568 = £22198; NI payable: 22198 * 12% = £2663.76.
Monthly income tax & NI payable: (3839.2 / 2663.76) / 12 = £541.91.
 Annual income: 18700 * 12 = 224400;
Taxable income: 224400 - 132000 (personal allowance) = HK$ 92000.
Tax payable (before tax reduction): 50000 * 2% + 42000 * 6% = HK$ 3250.
Tax payable (after tax reduction of 100% up to HK$ 10000): HK$0.
 GOV.UK. Live tables on Council Tax. Available: https://www.gov.uk/government/statistical-data-sets/live-tables-on-council-tax.
Notes: Average council tax for a Band D property: 1259 (Average of London boroughs) + 364 (Greater London Authority) = £1623;
Monthly council tax bill for a Band A property: 1623 * 6/9 (Band A multiplier) / 12 = £90 pm;
Monthly council tax bill for a Band C property: 1623 * 8/9 (Band C multiplier) / 12 = £120 pm.
The range varies wildly depending on which local authority the property is under.
 Rating and Valuation Department, Hong Kong SAR. Rates and Government Rent Calculator. Available: https://www.rvd.gov.hk/en/our_services/calculator.html.
Monthly rates bill for a property with a rateable value of HK$186,000 (12 x average monthly rent, see ), after (near permanent) concession: (825 + 825 + 1325 + 1325) / 12 = HK$360 pm.
 Ofgem, UK. Decision on revised Typical Domestic Consumption Values for gas and electricity
and Economy 7 consumption split (2020). Available: https://www.ofgem.gov.uk/sites/default/files/docs/2020/01/tdcvs_2020_decision_letter_0.pdf
 Ofgem, UK. Benchmark Maximum Charges for the Eighth Charge Restriction
Period. Available: https://www.ofgem.gov.uk/sites/default/files/2022-02/Default%20tariff%20cap%20level%20-%201%20April%202022%20-%2030%20September%202022.pdf.
Notes: Assuming standard credit. Gas bill: 111.35 + (1016.31 - 111.35) / 12000 * 8000 = £714.65 pa;
Electricity bill: 129.47 + (1051.00 - 129.47) / 3100 * 1800 = £664.55 pa;
Monthly bill: (714.65 + 664.55) / 12 = £114.93.
 Electrical and Mechanical Services Department, Hong Kong SAR. Hong Kong Energy End-use Data. Available: https://www.emsd.gov.hk/filemanager/en/content_762/HKEEUD2021.pdf. Page 37.
 HK Electric. Residential tariff. Available: https://www.hkelectric.com/en/customer-services/billing-payment-electricity-tariffs/residential-tariff.
Note: Electricity charge for 267 kWh of electricity per month (Aug 2022): 0.674 * 150 + 0.813 * 117 + 0.553 * 267 (Fuel clause charge) = HK$343.87.
 CLP Power. Bill calculator: Residential Tariff. Available: https://www.clp.com.hk/en/residential/bills-payment-tariffs-residential/bill-calculator.
Note: Electricity charge for 534 kWh of electricity every two months (Aug 2022): 0.87 * 400 + 1.004 * 134 + 0.482 * 534 (fuel cost adjustment) = HK$739.92 (= HK$369.96 pm).
 Towngas, Hong Kong. Tariff. Available: https://www.towngas.com/en/Household/Customer-Services/Tariff.
Note: Gas charge for 405 MJ of town gas per month (Aug 2022): 0.2725 * 405 + 0.0525 * 405 (fuel cost adjustment) + 9.5 (monthly maintenance charge) = HK$141.13.
 Energy Saving Trust. At home with water. Available: https://www.energysavingtrust.org.uk/sites/default/files/reports/AtHomewithWater%287%29.pdf. Page 13.
 Thames Water. How we bill you if you have a meter. Available: https://www.thameswater.co.uk/help/account-and-billing/understand-your-bill/metered-customers.
Note: Monthly bill for 8.66875 m3 of water per month: 8.66875 * (1.5415 (water) + 0.9488 (wastewater)) + (21.05 + 63.58) / 12 (fixed charges) = £28.64.
 Water Supplies Department, Government of Hong Kong SAR. Virtual Water. Available: https://www.waterconservation.gov.hk/en/why-save-water/virtual-water/index.html .
 Water Supplies Department, Government of Hong Kong SAR. Water & Sewage Tariff. Available: https://www.wsd.gov.hk/en/customer-services/manage-account-and-water-bills/water-sewage-tariff/index.html .
Note: Monthly bill for 31.6264 m3 of water per 4 months: (12 * 0 + 19.6264 * 4.16 (water) + 2.92 (sewage))) / 4 = HK$34.74.
 comparethemarket.com. Our best broadband deals. Available: https://www.comparethemarket.com/broadband/. Note: Unaffiliated.
 TelcoCheck. Best Broadband Deals – Hong Kong’s 6 Internet Service Providers. Available: https://www.telcocheck.com/blog/broadband-compare-eng/. Note: Unaffiliated.
 Housing Bureau, Government of Hong Kong SAR. Housing in Figures 2021. Available: https://www.hb.gov.hk/eng/publications/housing/HIF2021.pdf.
 Transport and Housing Bureau, Government of Hong Kong SAR. 2020 Rent Review of Public Rental Housing (PRH). Available: https://www.legco.gov.hk/yr19-20/english/panels/hg/papers/hg20200706cb1-909-1-e.pdf. Page 8, Note 6.
 Department of Leveling Up, Housing & Communities, UK Government. English Housing Survey: Social Rented Sector, 2020-21. Available: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/1088500/EHS20-21_Social_Rented_Sector_Report.pdf. Paragraphs 1.2, 1.4, 3.15, 3.16, 3.20, and 3.22.
 Office for National Statistics. Consumer price inflation, UK: August 2022. Available: https://www.ons.gov.uk/economy/inflationandpriceindices/bulletins/consumerpriceinflation/august2022.
 Census and Statistics Department, Government of Hong Kong SAR. Monthly Report on the Consumer Price Index: July 2022. Available: https://www.censtatd.gov.hk/en/data/stat_report/product/B1060001/att/B10600012022MM07B0100.pdf.
 Ofgem, UK. Ofgem updates price cap level and tightens up rules on suppliers. Available: https://www.ofgem.gov.uk/cy/publications/ofgem-updates-price-cap-level-and-tightens-rules-suppliers. Note: Headline cap rate increased from £1971 to £3549, a 80% increase.
 Prime Minister's Office, 10 Downing Street, Department for Business, Energy & Industrial Strategy, and The Rt Hon Elizabeth Truss MP. Government announces Energy Price Guarantee for families and businesses while urgently taking action to reform broken energy market. Available: https://www.gov.uk/government/news/government-announces-energy-price-guarantee-for-families-and-businesses-while-urgently-taking-action-to-reform-broken-energy-market.
Note: Headline cap rate increased from £1971 to £2500, a 26.8% increase.
 Using HK Electric's tariff:
Electricity charge for 267 kWh of electricity per month (Mar 2022): 0.674 * 150 + 0.813 * 117 + 0.345 * 267 (Fuel clause charge) = HK$322.84.
Electricity charge for 267 kWh of electricity per month (Sep 2022): 0.674 * 150 + 0.813 * 117 + 0.638 * 267 (Fuel clause charge) = HK$366.57, a 7.6% increase.
 Using CLP Power's tariff:
Electricity charge for 534 kWh of electricity every two months (Mar 2022): 0.87 * 400 + 1.004 * 134 + 0.397 * 534 (fuel cost adjustment) = HK$694.53 (= HK$347.27 pm).
Electricity charge for 534 kWh of electricity every two months (Sep 2022): 0.87 * 400 + 1.004 * 134 + 0.496 * 534 (fuel cost adjustment) = HK$747.4 (= HK$373.7 pm), a 13.5% increase.