What should we do ?

It may have an identification chip and a vet or the RSPCA will probably have a chip reader. I once came home to find my two neutered male cats looking after a skinny little female cat in my garden. I didn't recognise her as a local cat, so took her to a Cats' Protection place where they told me she had recently had kittens and that they would spay and rehome her. I was so sad that some rotten person had taken her kittens away and abandoned her.

If the cat is so thin but picky about eating it may need a vet's attention in case there is something seriously wrong. Our cat Smudge visited several houses despite wearing a collar - the children at one house called her Ribbons! Needless to say, we realised what was happening when she started putting on weight. This cat doesn't sound well.

Our cat Max had kidney failure and was on a special diet - he would visit people looking pitiful looking for whiskas, which they gave and hastened his end.
Try putting a collar on with a note in a cylinder asking the owner to call - if no call within 24 hours, I would take it to the vet, or contact cats protection - they will often rehome the cat with the finder when cat is better

If none of your neighbours know anything about the cat I would contact the Cats' Protection or a vet. She (with that colouring she is most probably female) sounds as if she could be ill. If she is not eating the thinness could be due to kidney or liver problems (in which case giving her ordinary cat food might not be a good thing) or she might have bad teeth and just not be able to chew. Are you leaving some water out for her as well?

Thank you cat lovers...I like the idea of a note with a collar and take heed about feeding it the wrong food iiiiiiif it is ill , Cat Protection are coming back to me . Will let you know how we get on.

Well puss cat seems to have disappeared, not been in the garden all week, don't know if something has happened to it or owners on holiday or... Looked in sheds and asked around but no one seen him, I'm consoling myself by thinking at least we stroked it and tried feeding it.

She could just be very old and ill, which would explain the thinness and poor appetite.

Sods law in action ! about three hours after I posted yesterday, who should wander down the garden path and come inside but puss cat, very friendly wondered if it's owners had been away for a week.

Son and I had searched our garden, bushes etc and under the sheds in case it had had an accident or even died.

Not seen today but at least we know it is still with us.

Sounds like you are doing all you can. We fed and finally took in a rather beautiful cat that looked ill. Took it to the vet and it really was ill, had a giant tumour inside, which was why he couldn't eat much. Had to be put down. Cost us over £100 [this is about 16 years ago.]If yours is ill you could be in for a hefty bill at the vets, and the RSPCA often put down even healthy animals, so the Cats Protection League would be the best bet.Good Luck.

Thanks for advice, we no longer have a dog because of fear of the huge Vets fees that can arise,I am trying to find out if any neighbours know where the cat comes from , still visiting and likes a friendly word and stroke. Can't animals get to you !

It sounds like you have a friend there bimbadeen our cat felix was very fond of visiting neighbours and putting on the "I'm hungry look" what a con-artist he was !! and yes they do get to you indeed, it may not be too long before you are off to the cats Protection Centre looking for a little friend to call your own.