I was lucky enough to get an assisted place at a (day) secondry private school.
I found the place far from snobbish. In fact 1/3 of the pupils attending were on some sort of financial assistance from the government at the time.
My school was ethnicly diverse. I mixed with kids from Muslim, Hindu, Jewish, Catholic, Protestant, Jainist, Buddhist and athiest backgrounds and who came from all over the Midlands. It's only later in life, I appreciate this because as kids we all mixed together without prejudice.
The alternative would have been an all Catholic school with peers from roughly the same neighbourhood.
I would happily send my kids to a private school.