The best performing schools, hence being oversubscribed, in my borough are "ordinary" schools both at primary and secondary.
Plenty of CofE and Catholic primary schools, inspected under the new OFSTED rules, have been down graded from good to satisfactory and outstanding to good, due in a large part to "cruising". This is often caused by staff staying in situ too long.
Like anything, there are good and bad but I've always believed that religion has no place in education, as per the French model.