If they offer similar results, I would suggest going to your local school. Two hours a day is a long time to spend every day travelling to and from school; that's 10 hours a week. It's less stress and although Henrietta Barnett School may be a higher prestige, chances are the school you are considering going to closer to where you live is of a good rating (I assume).
I believe that UCAS only know whether you went to a state/private school, not the school you actually go to (someone please correct me if this is wrong!). Remember employers only care what grades you get, not where you go to.