I have found a few wallets, mobile phones and bits of jewellery in my time. Always handed them in if there was any chance they could be claimed. Random cash (ie tenner on the pavement) is fair game though.
Years ago, when filofaxes were a thing, I found one on a bench in a park. I waited for ages but there was nobody else around at all. Seeing that there were credit cards in there, I decided it would be easy to track the person down so took it home. This was pre-google so although I had the name of the owner, I was leafing through all the plastic pouches, pages and pockets and a gazillion business cards for a phone number or clue as to how to find them. Right at the back there was a zipped leather flap thing and when I opened it, it was FULL of money. £12K
Twelve actual thousand pounds.
I rang my mum and we went through the thing again and finally found a business card that matched the name on the credit cards and it was a local clothes boutique. We went there with the filofax and asked if they were the person whose name we had. She was and when we told her we had her filofax and she saw that all the money was there, she burst into tears. It was two month's worth of shop takings that she'd taken out of the safe to bank.
She gave me and my mum a £500 gift card each to spend in her shop. we were both far too chunky at size 14 for any of her pretty size 6 clothes, so had to buy lots of bags, belts, hats and earrings It was amazing though - like doing a trolley dash!