The distances should be in the primary school admissions handbook, which is available on the council website if you don't have a copy. Or the schools will be able to tell you if you phone them.
Purley oaks does have a bad reputation, so do go and have a look. It suffers from high pupil and staff turnover. Parental engagement isn't great, because it has a lot of esl families - no PTA, as far as I know.
Haling hasn't been open long. I'd go and have a look there too. I don't think it is oversubscribed.
St. Peter's is a lovely school but very popular. It recently went two form entry, which has helped a bit, but if Purley oaks is your nearest school, you probably are too far to get in, even on a waiting list.
Have you considered Christ church? That is now two form entry, and depending on where you live, you may be able to squeak in. If you go to church, you have a better chance! Have a look at the admissions criteria. Nice school, currently a building site though!
You may also be in with a chance at ridgeway - an outstanding three form entry school, according to ofsted, and very popular - and Regina coeli, which is Catholic but does take non-church goers. Regina recently had an ofsted that didn't go well, but there is a lot going on to make it better.