If you can catch it, take to the vet to see if it has been chipped, for details of the owner. If you don't have a suitable carry cage, if required, the local animal charities will usully loan one out to you. Good luck.
Hi a similar situation happened last year where a black cat was hanging around Union Street for weeks and was being kindly fed by neighbours until Battersea came and took him into care. If the cat is a stray then please call the Battersea Dogs & Cats home and they will come and collect the cat for rehoming.