As Dzug states, items valued at less than �18 don't attract charges. Otherwise, there can be substantial charges to pay.
As an example, let's say that you buy some clothing for US$100 (roughly �50) and pay US$30 (about �15) for shipping.
HMRC start by calculating the import duty. On some items this can be very low but clothing normally attracts duty at 12%. However, the UK is currently imposing a trading sanction on imports of cotton-based goods from the USA. (This is because the USA is breaching World Trade Organization rules on subsidies to cotton farmers). So the current rate is 27%.
27% of �50 is �13.50.
Next, HMRC calculate VAT at 17.5%. This is charged on the goods, on the carriage and on the import duty. (Yes, that's a tax on a tax!).
17.5% of (�50+�15+�13.50) = �13.74.
Lastly, they charge a flat-rate fee of �8, for the privilege of having them inspect your goods!
�13.50 + �13.74 + �8 = �35.24. That's the amount the postman will demand before handing over your goods. (So your �50 item will cost you a total of �100.24, including carriage and import charges).
Import duty isn't charged on items valued at less than �18. VAT isn't levied if it comes to less than �7. The �8 flat fee is waived if there's no duty or VAT to pay. Putting all of those together means that anything valued at less than �18 doesn't attract any charges. (A few items, such as books, don't attract import duty or VAT, so there's no limit on the value of such items which can be imported without charges).
Chris