If you go to
www.upmystreet.com and plug in your post code, you'll get a listing of all the schools in the area. I know when we got here, the closest schools for the younger one were oversubscribed, so he ended up in our 3rd choice, but it's still close enough for him to walk and it's turned out great because the older one's school is right next door!
As for the older one - we moved in September and didn't get him in school until December. ALL of the secondary schools were oversubscribed, so it had to go to a committee that meets only once a month! Argh. We hired a tutor for him in the meantime, which worked out well. Anyway, we were told there was no *guarantee* we'd get the school we wanted, but we could put down our reasons for wanting it and that would be considered. And we got it. But the *poor* boy was out of school for a full 6 months! (The let out last day of May at his school in Florida and he didn't start again until the beginning of December!).
Anyway, go to that link and get the school listing. And talk to the headmasters, because even if the school's "numbers" don't look all that great, you need to find out if there are extenuating circumstances. I.E., my youngest's school has a separate language centre for kids who don't speak English as their first language or have speaking/reading disabilities. And their test scores are added in with all the others, so that obviously will bring the school's average down as a whole. Even so, the scores weren't that bad, really. And he's thriving there, so we're happy!