If you reject the place, then you run the real risk of not having any place for your son come September.
The reason he did not get in because all the other schools on his preference list were not in catchment and they gave a randomn
It's a common misconception amongst parents that the LEA will have to give your child a place from those you expressed a preference for. They don't have to.
What they must do is, for each school, allocate the number of places the school can admit to those children who have the highest priority according to each schools admissions criteria.
It sounds like all the schools you'd put down gave their places to children who lived closer to the schools (or had siblings already attending, if that's part of the preference). That's why for both primary & secondary / grammar preference forms I always strongly recommend that a parent puts the local catchment school down somewhere on the list, even if it's last choice, so that if the worst happens, at least your child should have a place at a local school.
If not, what happens is what you've discovered - your child drops to the bottom of the list and is offered a place at the closest school with a space once all children who have expressed a preference for it have been given places
. In rural areas such as mine, that can mean a trip of 20 or 30 miles each way!
I would strongly urge you to accept the place offered, and then as well as asking to go on the waiting list for other schools, consider an appeal for other schools closer to home. Be warned, though, that Key Stage One appeals can be hard to win, as there is a limit of no more than 30 children in a class, which can only be overturned if an error was made by the LEA (which is very unusual), or the decission not to allow the place was not a reasonable decission (again, very unusual). I'd say it's harder to win an appeal for a primary where the 30-in-a-class limit has been applied than a grammar appeal!
If the intake is not 30, multiples thereof, or 45 (so a split Reception / Y1 class), then your chances at appeal may be slightly higher.