When importing items from non-EU countries by post you get clobbered for Import Tax (the rate of which varies depending upon the types of items being imported), VAT and a customs examination fee (typically £8).
However the rate of Import Tax on books is zero, VAT on books is zero and the customs examination fee is waived when there's no Import Tax or VAT to be paid.
So you won't get charged a penny for importing your books from the USA. (I've done it plenty of times myself).
However you need to take care if you're ever considering importing certain other items. For example, if you imported cotton-based clothing from the USA, to the value of £200 with £20 carriage, you'd get clobbered for the following:
12% Import Tax (applied to all non-EU countries) = £24
15% additional Import Tax (as a punitive trade measure against the USA because it is in breach of World Trade Organisation rules through providing subsidies to US cotton farmers) = £30
VAT at 20% (charged on £274, because that's the value of the goods plus the price of the carriage plus the Import Tax) = £54.80
Customs Examination Fee = £8
Total to be paid = £108.80
Take care when buying from outside of the EU. (If we don't negotiate a customs union with the EU as part of Brexit, similar rules will soon apply to imports from EU countries too). It can get very expensive!