Anything in a wallet would be handed into the police. Notes and coins I have kept in the past. No point taking £20 to the police station,. Who honestly would go to the police to say 'I had £20 in my purse earlier and it isn't there now'.
If it were a wad of cash, ie lots of £20 tagged together, it is best to hand it in. 1. because it could be fake 2. it could have been stolen from a bank robbery and the numbers on them will mean they are being tracked and you can expect a police van pulling up at 7am outside your house.
I found a wallet before it had £2000 in it complete with gold credit cards. Returned it and the guy gave me £100. Split it between my ex wife and I and we had a good night out.