@cbcole the reference to "middle class secondaries" in the previous post is unfortunate, and may take some explanation to someone coming from abroad.
Many UK schools manage oversubscription by prioritising admissions by distance. So if one school gets a slightly better reputation than another, people may move nearby (just as you are considering doing). Over time, the demand for nearby properties causes prices to rise, so that only wealthier people can afford to live close to the school. Because this is England, some people refer to these people as "middle class", but it's a crude use of the term. They should say something like "relatively wealthy" instead.
There isn't a direct correlation between wealth and class - you can be middle class and relatively poor, and you can be working class and relatively rich. Class is a vague concept, with varying definitions, but is as much to do with your education and family background as it is to do with your financial circumstances.
Anyway, back to schools. Not all schools prioritise admissions by distance. Some schools use other criteria, e.g. faith schools may use proof of church attendance. You need to look at the admissions policy for every school of interest - it will be on their website - to see how they prioritise.
I have friends with children at King's School, Hove, which I believe prioritises 50% by church attendance and also uses distance. They are atheists, but they are very happy with the school - they say it is very inclusive.and their children are doing very well there.