As the UK is a member of the EU (for the time-being, at least), the Import Duties applied by HMRC (for imports from non-EU countries) are those set by the EU. They can be found here:
http://ec.europa.eu/taxation_customs/dds2/taric/taric_consultation.jsp?Lang=en
(Click 'Browse' to search for the relevant classification).
However there is no duty to pay when the value of the goods comes to less than £135.
VAT (at 20%) is charged on exactly the same things that attract it in the UK. That's basically everything except books, periodicals, children's clothes, non-luxury foods and a few other items.
However VAT isn't charged when the value of the goods is less than £15. (NB: Note that VAT is charged on the goods AND on the carriage charges AND on any duty payable - Yes, that really is a tax on a tax!)
Then there's a customs examination fee to pay, which is usually £8.
So you'll ALWAYS get hit for import charges when buying from non-EU countries unless they're valued at less than £15 (or, if they're exempt from VAT, at less than £135) .
For example, if you buy something for £20 (+ £5 p&p) , you'll have £5 VAT to pay (= 20% of £25) plus an £8 examination fee, making £13 in total.
As a further example, if you were to by cotton-based goods from the USA, valued at £200 (with £20 p&p), you'd be charged the normal rate of Import Duty for cotton-based goods (12%) plus an extra 'penalty rate' (15%) applied by the EU because the USA is in breach of World Trade Organisation rules in respect of state subsidies to cotton farmers. (So that's 27% of £200 = £54). Then, assuming that the goods aren't in the form of children's clothing, there's 20% of (£200 + £20 + £54) to pay (= £54.80). Adding on the £8 examination fee produces a total of £54 + £54.80 + £8 = £116.80.