in short, NO!
look at your Police Service FOUND PROP policy and find this wording:
Found by Police/Police Staff
Police Officers and Police Staff finding property either on or off duty have no claim in the event of an owner not being identified.
No person employed by a police authority may acquire or enter into any negotiation to acquire any property found or seized, either by way of gift or by purchase (except by public sale), without the authority of the Chief Constable.
PCSOs should know this inside out, no police staff including PCSOs can claim found property in the event that a loser remains unidentified.
This PCSO who found a £20 note in the street and handed it in CANNOT CLAIM IT!