Are there any in-between tax bands or would my income tax be either 0,20,40 or 45% ?
If (in 17/18) I make 44999 a year my tax would be ~9000 but if I make £2 more at 45001 my tax is now ~18000 ?
Warning, if you earn between £100k and ~£120k then you will pay 62% marginal tax. Let me break this down. There is 40% for that band but then there is the withdrawal of your personal allowance at half speed meaning an extra 20% in the said band. Then there is 2% Employees National Insurance (NI) on high incomes.
Come to mention it, you haven't reference National Insurance (NI) at all. The NI bands shadow the Income Tax bands. So if you land in the 20% Income Tax band then you also have to pay ~13% Employee NI, this assumje that you are employed and not taking income as dividends from a company (even then rules apply (IR35)).
Anyway, there are plenty of UK tax and NI calculators, top of list is this one The Salary Calculator. It looks good enough.
Your tax rate is a lot lower than you assumed.
In 2017/18, the first £11,500 of income are tax free. For the next £33,500 from £11,500 to £45,000 you pay 20% tax. For the next £55,000 from £45,000 to £100,000 you pay 40% tax. Above that it gets a bit complicated...
If you make £45,000 then £11,500 is tax free, and you pay 20% of £33,500 = £6,700 tax. If you make £45,001 then you add 40% of £1 to that, which makes it £6,700.40.
However, you also pay employee national insurance of 12% on income from £8,164 to £45,000 and 2% on income above that. That is £4,420 for the income up to £45,000, and two pence for the next pound.