This is not the only reason, schools like these, all girls or all boys tend to be better off as it is, their parents established middle and upper class. They come from well to do backgrounds and they pay extortionate amounts of money on fees. The standard of teaching is higher, the discipline standards are higher.
Take a look at the school this headteacher is speaking from:
Fees per year: £11,900
That's more than the cost of University tuition fees.
Please don't go comparing this to your average, underfunded, overpopulated, state run, inner city school.
No sane comparison can be had.
And I have seen these private schools up close, they some universities in the UK look like homeless shelters.
Seriously, go to one of the few in London, get a taste of what it would be like if you had the title of 'Lord', earned 6-7 figures minimum, and sent your kids there.
Anyway, with that said, it is true that schoolgirls in the UK and British females in general seem to spend unholy amounts of time and effort on their looks, appearances, social contact, and having no boys around must help. But let's not kid ourselves, look at the elephant in the room.