You'll need to have more than just the same blood group. Any prospective donor has to have their cells tested against those of the potential recipient ("tissue typing") to see if there are sufficient genetic similarities for a transplant. The chances of any random individual being able to provide a sufficiently good match are extremely low. (There will probably be only a handful of possible donors available, if any, from the 400,000 registered donors in the UK). It's usually only close family members who might be able to become donors. (Even then, there's no certainty that a family member will have a sufficiently close genetic match).
Your doctor will only know your blood group if there's ever been a reason to record it. If he knows it, you'd have to ask in person as no doctor would give out personal information to a phone caller.
Chris