No private school can really afford to be labelled as "non academic". It would generally be like signing a death warrant in London!
From my experience of schools labelled "less academic", people are very adept at getting their bright children to shine at them. They like the slightly smaller pond and slightly lesscompetition. No beating yourself up all the time. Children do not need to be around 100% bright children to thrive.
All schools want academic pupils.They want good results and stellar universities for as many as possible. No school these days can make a selling point of 50% into university of some description and the rest into the local college of FE. Many people want their not so bright children to rub shoulders with the brightest and go to the "best" schools. In order to do that, they have years of tutoring. I totally agree with Xenia that it is the wrong thing to do.
Both mine boarded at Queenswood School in Hertfordshire with no tutoring at all. Not before, or during. They stood (or fell) by what the school could teach them. The great thing was all the other activities they did. I saw one very gifted child there (in 10 years as a parent) who was not stimulated. She was definitely in the wrong school because her behaviour deteriorated and she hated rules. All schools have rules of course, so kicking against rules will always make life difficult!
Do look at Queenswood. It always has enough bright girls and, quite frankly, so much else to offer, there is no need to ever be bored or not stimulated in another way outside of academics. For example, drama, music, sport, leadership, debate, House events. There is a huge array of activity for girls and the brightest are often leading the way! Its a hugely supportive community.