Sorry, hit the submit button by mistake.
The wallet not being important enough to justify a warrant, the police can only wait until the owner reports it lost and can identify it as his/hers if the police happen to have 'found' it. If it's not claimed within a certain amount of time then the finder has the right to take ownership.
I would imagine, in the case of a mobile phone, they would have to remove the SIM and clear the phone's memory first if they were to do this.
As to whether or not it's a common law right to claim ownership, I wouldn't know, but I'd be interested to find out.