From HMRC's website on things brought in from outside the EU. This is over and above your allowance for tobacco and alcohol.
"Other goods including perfume and souvenirs
You can bring in other goods worth up to £390 without having to pay tax and/or duty.
If you arrive by private plane or private boat for pleasure purposes, you can only bring in other goods worth up to £270 tax and duty free.
If you bring in any single item worth more than your allowance, you must pay duty and/or tax on the full item value, not just the value above the allowance. You also cannot group individual allowances together to bring in an item worth more than the limit."
That's per person. Inside the EU there is no limit. I always put stuff in hold baggage, and like the idea of having the receipts on the top of the boxes/bags as it shows you are being open about what you are doing which often helps with any conversation at Customs. HTH
