I would hand it in at the police station, I know I would.
However - why don't you join one of these insurance schemes to protect your cards? I belong to CPP, all my cards are registered with them, and if I lose my cards I don't need to ring all the individual card issuers, one call to CPP and it's all done for me. Lots of card companies offer cover but this is the one we use
http://www.cpp.co.uk/
It's a vile feeling - my purse was stolen from my zipped handbag in Spain last year.