The cat I observed was taken away by the RSPCA for veterinary treatment. He had no microchip, and they assessed him as semi-feral. I passed on the contact numbers on the paper that came through my door, and I haven't heard any more from the RSPCA person since then. They were planning to contact the people, I'm sure.
They won't have re-homed him to anyone else, as they were asking me if I would take him on as an outside cat and I said I would, if his owner couldn't be traced.
Sadly there is no way of directly contacting the RSPCA officer, I have to wait until she rings me.
If the family are still looking for their cat they need to contact the RSPCA on their general welfare number and tell them they think their cat may be with them.
0300 1234 999 should get them.