The simple answer is that VAT is not only for UK citizens but for any goods (and services) sold or coming into the UK/EU. For goods produced or sold in the EU, the company selling it takes care of the VAT for you (but you are paying it). For goods you are importing yourself, you have to take care of the formalities yourself.
Beyond that there are a few quirks in the system, some allowances for things private persons carry with them for non-commercial purposes, possibly different rules if you are only staying a very brief time or bringing stuff with you as part of a move to the UK and of course not everybody who disregards the rules gets caught but the principle is simple: VAT must be paid when importing stuff into the UK, even as a non-citizen.
Of course, in the EU, you can always walk through the green channel and get lucky. Only a small proportion of all luggage is searched and a small number of travellers are questioned, there is no need for everybody to fill in a landing card or talk to a customs officer like there is in some other countries. But that's just a matter of enforcement tactics, not a proof that there are no limitations on what you may import (see also Why do some countries require everyone entering to see a customs officer, and some don't?).
And if you think you are home safe because you brought something over the border once, read Ridiculous and unreasonable taxes for used electronic devices in europe. You can still be taxed, possibly even forced to pay some penalty, many years from now, if found out.
Finally, it's natural to want to know the rules in advance, have an idea of what it might cost you and avoid the hassle of going through the red channel if you can avoid it but you can also simply ask this question to a customs officer on arrival. If you are covered by an exemption, they will tell you, there is no downside in approaching them when you are unsure.