IIRC, in the UK, if you unwittingly buy a stolen car, it still belongs to the original owner. The police can take it from you and give it back to the original owner, without reimbursing you for it.

Could be, I'm not up to date on UK law. But over here it's like that. Of course, I did say when the stolen goods are bought in good faith.
A car always comes with certain documents through which you can almost immediately tell if something's fishy or not. If those documents are not ok, or they are missing completely, accompanied by an offered price that is way less than the car is worth (even second hand) then the law states that that should have rung a bell.

If it didn't and you buy the car anyway, you'll loose the protection of the "in good faith" clause, and the car can be taken away from you. ('cause the law figures "nobody can the that stupid") You'll probably even get sued yourself for fencing (is that the correct term?) stolen goods (and rightfully so I say!)