Thanks for your reply Magenpies and for some great suggestions. I started with Balham Streetlife and moved on from there to other forums and am now feeling like a Pet Detective! No luck so far but I might take her/him to a vet to see if theres a microchip.
Im also trying to get a decent picture that shows all her distingushing markings, will post when I have some success!!

BoPeep. I don't suppose you could try and get a photo of the cat the next time it visits you - and then post the photo here?

(I know it isn't my B&W cat because he wouldn't venture that far - nor does he go missing! We are a 'fair stretch' further away - in cat terms - even though I know they wander!)

Also, do you belong to Balham Streetlife? https://www.streetlife.com/area/balham/

It's another good, local forum and there are frequent posts about lost and found cats/pets - so it might be worth your while posting on there too.

I know there's a cat who lives in Hearnville Road who likes 'visiting' - but I haven't seen it for yonks and can't remember its colouring now.

Although maybe the owners of the small shop on Chestnut Grove might be familiar with your visiting cat?!

A rather lovely and quite mature black cat with white paws and a white diamond on her chest has taken a liking to our house in Fernside Road. To our children's delight she is constantly outside the back door mewing to be let in or even sleeping on their first floor windowsill at night. We went away for 11 days and found her at the back door on our return. He/she (!) is well fed and in very good condition. I rather suspect its a case of 'Six dinners Sid' and he/she has several favoured houses which she visits when it suits. We do not feed her as she is not ours and she seems well fed. I just worry that an owner is wondering where she gets to - if thats you do let me know.