I'm gonna make a bold statement here:
I think Oxbridge pick people out of a hat.
Am i the only one whose teachers are really supportive for anyone going for oxbridge?
P.S. your school shouldn't matter as to whether or not your GCSEs are all A***** , but unfortunately it probably does. But overall I think your GCSEs will only have an effect on getting an interview, after that it'll be mostly Alevels and the interview/tests/written work. If you go for a subject that isn't med/vet/law (although eng might just fall into this category) you're v. likely to get an interview - my school has never had anyone not get an interview (we only send 4-5 people a year).
I think Oxbridge like things like that because it shows you have actively been trying to improve since school.