Surprisingly, the good ol' Nationwide Building Society will do it ... But you'd only want to set up the necessary accounts if you're going to be doing it regularly. It can all be done on t'internet.
You need to open a euro account with Nationwide International, in the Isle of Man - and a flex-account (regular bank account) with Nationwide on your high-street. You'll need to 'authenticate' yourself with a passport, which you can show at your local branch.
Swift transfer your Euros into your "offshore" account (will cost you £20 a time, as said).
When you feel like trading, phone them up and say - "convert 20,000 euros to pounds".
And they do ... it appears instantly as cleared funds in your online flex-account.
They do good rates too - I do it in Dollars but their rates are within 1/5th of a cent of the money-market rate.