i'm not rich enough to own a house and mews
more seriously, that.
some cats who already have someone who considers themselves an 'owner' are fairly good at turning up on other peoples' doorsteps claiming to be a poor hungry stray kitty.
while i'd not want to turn away a genuine hungry stray, feeding cats that 'belong to' other people can be awkward. i'm on friendly terms with two neighbour cats, but i don't feed them or give them treats, and don't invite them in - both will occasionally wander in if the front door's open, but i have escorted them out again.
if kitty does have a home, they may need to follow a particular diet, some cat 'owners' get offended if other people feed 'their' cat and the law is a bit fuzzy, but i think you could get done for theft if you just adopt a cat that already has an 'owner'. some cats refuse to wear collars (one time kitty that lived with my long time ago partner could 'lose' a collar within an hour)
although some people accept that 'their' cat is only on a time share basis - i have a friend who's got a cat (that theoretically has a home) that turns up every week or two and stays a couple of nights then buggers off again - he has managed to trace the 'owners' and they are quite relaxed about it and have even offered to contribute towards kitty's board and lodging.
may be worth asking round the neighbours. or a 'found cat' notice either physically or on local farcebook or whatever if you do such things. and if that doesn't get any response and kitty hangs around, then they need to go to a vet or a cat rescue centre or something to see if they have a microchip.
cats protection have more on dealing with unexpected kittehs.
but it could be that the cat distribution network has decided it's time you had a cat...