If you buy something new in Europe that you're bring back to North America, you can declare that before you leave and get the VAT returned to you. I'm not sure you can do the same going out of the US though.
But any of these times you returned to the UK, you were probably given a declarations card to fill out, stating how many good you purchased and are returning with. If you don't list something you're supposed to declare that is in fact a crime. Maybe a hard one for them to prove that you didn't have an Axe FX III when you left and you're just returning with it, but you are still supposed to declare it and pay the VAT.
That's why anytime you order it shipped (and therefore can't lie that you already owned it) or a company imports it they have to pay the additional taxes and duties, and part of why buying domestically is more expensive: they have a harder time illegally importing goods that you.