I don't think any college is supposed to use your school as a criteria for admission, either positive or negative. There are some colleges which typically have a greater proportion of students from state schools (King's typically has the most, I think I've seen some statistics comparing them all, but I can't find them at the moment), but this is only relevant if you would rather be around more or less state school pupils (even this doesn't matter, once you get in no-one cares which school you're from).