Where do you live, MrsCrisper?
Do put down a little food, and more importantly, water - I am hoping that someone is doing this for my missing cat.
A stray cat is more likely to go to a house with other cats, in the hope of finding a nice person and some spare food.
See if you can gain its confidence and perhaps be able to get it to stay in your garden (is there a shed?), then you can call the local vet and/or pet rescue and see if a cat fitting this description has been reported. Even if he doesn't stay in your garden, someone (like me) will be glad to know of a sighting even if you can't catch him.