Ordinarily I think the school you would most likely got into would be Lee Manor. They have their summer fair on Sunday the 12th of June I think, so you might like to double check their website and go along to it. (I don't know your exact distance from the school though)
Just double checked admissions criteria for St Margarets, and it seems the religious admissions criteria is now less onerous. Only attendance at least fortnightly for only 1 year, but if your application needs to be in by the end of January 2012 it looks like you won't be able to fulfill that. It does make me think that it is more likely they will fill the 10 religious places, when they haven't for the past 2 years.
Also, bear in mind that both Brindishe and Lee Manor had bulge classes. That means Lee Manor's catchment was really wide this year, as extra kids got into Brindishe that would of normally gone to Lee Manor. Both schools catchment areas are going to contract accordingly because of extra siblings going to both schools that would normally live too far away. So nothing is gauranteed where you are moving too unfortunately. Funny position, close to lots of good schools but not quite close enough to feel safe about any. I think you will find kids living there go to different schools year on year depending on where there is extra space. The less desirable schools you would most likely be close enough to get into if you miss out on all the closer ones would be Brindishe Green (formerly Hither Green) or St Matthew Academy, so maybe as an insurance policy look at the less desirable schools too and put one down as choice number 6 just in case.
Still worth considering John Ball just in case they have a bulge class (you wouldn't get in otherwise), you never know where a bulge class might be allocated.
I am fairly familiar with my school admissions, I will be applying for my ds for entry 2013.
Congratulations on your house exchange, it is a nice area you will be living in. Just watch out for Pistachios though, lovely location in the park, not very clean though. A friend of mine got food poisoning from a crepe, and one worse story I won't repeat on the internet because it was a friend of mine and I am not sure if she wants the story repeated. I avoid it.