I've done it with my bank, Abbey (Abbey National as was) a few years ago, took out a personal loan saying it was to buy an aeroplane. The girl on the phone was quite amused, I don't think she'd heard that one before, but no problems at-all, money came through inside a week once I'd signed the paperwork.
So long as you are borrowing in the bracket £5k-£25k and are a homeowner, most of the banks are giving pretty much the same rates at the moment (a bit under 7%).
What are you planning to build?
G