I would like to fully understand the following passage from https://www.gov.uk/guidance/stamp-duty-land-tax-buying-an-additional-residential-property :
You must pay the higher Stamp Duty Land Tax (SDLT) rates when you buy a residential property (or a part of one) for £40,000 or more, if all the following apply:
it will not be the only residential property worth £40,000 or more that you own (or part own) anywhere in the world
you have not sold or given away your previous main home
no one else has a lease on it which has more than 21 years left to run
Question. Suppose the buyer in question owns half of one property (and that's it). Moreover, the whole property worth £50,000 (so its half worth £25,000). If they buy a flat in the UK (for >£40k) do they need to pay higher SDLT according to this passage?