Yeah, you can try. I would guess about half of bank branches would do a small number of coins for a random person and half would refuse, but I don't know any visitors who have tried in the past year.
We were in London again last month and still had a few old-style one pound coins that we brought along with us. Brought them into a Lloyds Bank branch, explained that we were Canadian visitors and the teller happily changed them. We were in and out of the branch in under 10 minutes.