From what I've know, St Paul's is religious (Church of England, VA) and the head teacher is fairly keen on religion. St Matthew's is not religious (despite its name) apart from what is required for any community school.
You would not be reassigned a school - all schools will have some small element of religion of a broadly Christian nature (often very minimal - a reading at assembly, or a few songs, sometimes focusing on general 'kindness' type values), and you are able to withdraw your child from this if you want. (In many schools, you'd barely notice it).
Schools such as St Paul's will give priority to those who attend church, but in practice, many lower down the criteria will also get in on distance, including those who do not practise any religion.
The council will have a list of which catchment various streets are in - it won't be both St Matthew's or St Paul's, but one or the other, and you will also have a slight priority if you apply to your catchment one. You could still get in on distance grounds, though, if the school isn't oversubscribed (e.g., if you are in St Paul's catchment, but prefer St Matthew's as it's less religious, and you live quite close, you might still get in). I don't know how oversubscribed they are these days. You are better off making sure you rent in a street that is in the catchment of St Matthew's, as you will then have a better chance of getting in (and the closer the better, as distance will be a tie-breaker within the category).