You must not assume this cat is lost, cats are very good at making out they are lost when they are not, it could well be a very local cat whose owners were simply out for the evening, or perhaps away for the weekend and had left a neighbour in charge of the cat. So see if it comes back and how it behaves. Only consider that it may be lost if it seems to want to move in with you (and don't try to encourage it to do so by providing gourmet food - something very basic will be eaten readily if it is really hungry)

On the other hand this cat could be many miles from home, if it has jumped in a workman's van, or been kidnapped and dumped by some vengeful gardener (yes there are people who openly boast on the internet about such actions). So if you keep seeing it and it really is hungry, the first thing you need to do is to take it to a vet to be scanned for a microchip. Explain the circumstances on the phone when you make the appointment, the vet should not charge you for scanning but it might be worth making sure first!

If there is no microchip then posters locally, an advertisement in the local newspaper (ours puts "found" ads in free of charge), ringing round the local vets, cats protection and RSPCA to see if one has been reported missing. I would not recommend handing the cat over to the RSPCA under any circumsntances, their record for destroying animals for no good reason is enough to make me avoid them like the plague, but they may have a report of a missing cat.

Finally if you have tried all those things there is a place on the internet where people list lost and found animals. I can;t remember where it is but a search should turn it up quickly.

Do let us know what happenes, won't you.

Liz