Does it look well fed? Have you stroked it yourself, can you feel the bones? (some cats are starving but hard to tell through the fur) Does it have clear bright eyes? If it seems ill or poorly I would probably consider keeping it somewhere (not in the house though as it's not fair to get it attached to you in the immediate term)- somewhere like a shed/conservatory/garage maybe, ideally with a cardboard box & old towel to sleep in, then ring the RSPCA/take it to vet tomorrow for scanning to see if it has a chip, it could be lost.
If it looks quite healthy and is a good weight, I would just leave it for now. It's not a freezing temperature out there fortunately at the moment and cats always find the warmest place. If it is still hanging around tomorrow ring the local vets to see if anyone has registered it lost. It could well belong to someone very local (within 5-10 houses) and is just being friendly. However it may be very lost and genuinely need help, so if it's still hanging around after 2 days I would contact RSPCA/vets/local cat home. The most important thing is to have it scanned for a chip.
Re the other cats and foxes, occasionally cats fight but that's more territorial, and foxes aren't well known for picking on cats, so I wouldn't worry about that.
There's a member on MN who is connected to the Celia Hammond trust, hopefully they will be along to offer some professional advice too.
Hi Jellykitten, thanks for much for the advice, you have set my mind at rest quite a bit - we don't have pets ATM so I am a bit clueless.
The cat seemed young, quite small, quite skinny but clean with lovely fur and bright eyes so I think definitely looked after and loved. I will not worry too much tonight but keep an eye out tomorrow and see if it's still there.
Thanks again for taking the time to advise, I really appreciate it