Use Btc-e?
That's not a UK bank and also requires ID?
It doesn't have to be a 'UK bank' just available to use in the UK.
Like ropbat said you can buy a small amount off bittylicious which is a UK based exchange. Why don't you try buy off the forum here? Go look in the Currency Exchange subforum and there's plenty of people with many different payment options, but doubt bitcoin will go right down to £175 if that's what you're waiting for.