Under the Theft Act 1968, a person is guilty of theft if they “dishonestly appropriate property [including cash] belonging to another”.
‘Lost property will continue to “belong to another”, unless it has genuinely been abandoned by the owner. The fact that cash has been dropped in the street does not necessarily mean it has been abandoned.’
However, he adds that in the end it’s down to whether you could reasonably believe the owner of the cash was untraceable, or you had already taken reasonable steps to find them – such as by going to the police.