This sort of happened to me, in the sense that I found a £20 note in a puddle in a supermarket carpark. There were no other cars (bar the one we were in) in that part of the carpark, suggesting whoever it belonged to had long gone and there was very little chance of them getting it back. So I took it, dried it out and kept it. There is nothing linking a note to who ever might have owned it so it would be hard for the police to return it.
However had the money been in a purse or wallet, especially if there are cards in there too (no matter if they are credit cards or student cards ect.) I would probably hand it in. Personally if I lost a note, I'd be very disappointed but think it would be unlikely I'd get it back. However, if I lost my purse with all my cards (debit card, student ID, proof of age, ect.) then I would put in a lot more effort to try and get it back and would hope it would be handed in, even if the money in it has gone, as whoever finds it has no use for my cards but it would cost me a lot of time and money to replace them all. Having cards in the purse/wallet also means it is a lot more likely to get back to it's original owner.