If you find money in the street (instead of in a shop with loads of CCTV cameras, which could have seen who dropped it), with no indication as the where it could have come from, you're probably within the law if you keep it:
"A person’s appropriation of property belonging to another is not to be regarded as dishonest . . . if he appropriates the property in the belief that the person to whom the property belongs cannot be discovered by taking reasonable steps"
[Theft Act 1968, Section 2]
(Note that as long as you have a genuine belief that it would be impossible to trace the owner you're in the clear. It doesn't matter if it can later be shown that the owner could actually be found; it's your belief that counts).
What would I do? Here are some actual examples of what I've done in the past:
(a) I spotted a £20 note on the floor of my local convenience shop in Sheffield back in the 1980s and handed it to the shopkeeper. He later told me that one of his regular customers, a lady well into here eighties and bent nearly double with back problems, had turned up very distressed because she'd lost £20 from her pension and she was delighted when he returned her money to her ;
(b) I spotted another £20 note in the doorway of a sub post office in Lowestoft, took it inside and handed it to one of their staff, who took my contact details. Three months later, as the money had been unclaimed, they posted it to me.
(c) I found £30 sticking out of one of the self-service tills in Asda (obviously forgotten by someone who had used the cash-back facility). I noted the number of the till and handed the money in at the customer service desk. (BTW: I've left money sticking out of a self-service till twice myself in Asda. On both occasions I got it back from customer services).
(d) My colleagues and I quite often found money lying on the ground at the railway station where I worked. It was always recorded in our lost property book and then handed in at the booking office. A guy turned up once to enquire about the US$200 dollars he'd mislaid the day before and was amazed when we returned his money to him.