@GoldieStar my daughter is at St.cats and we have her much younger (step) brother at Lanesborough (ps. Not sure about the new head....)
.....but anyway, practically wise the journey is a total bore/chore, however, it is, like someone else rightly said totally 100% doable. So you'll be fine commuting across. Although, as soon as DD hits 17, the driving lessons are starting, let's put it that way! Haha
School wise, we've never regretted St.Cats, as when we joined (year 10 now) it was a really great choice. It's done my daughter very well, however despite this i would have reservations about making the same choice again now. The school just hasn't changed since she started, the routines rules and 'traditions' are the same, it's all become a bit boring and most of the time rules seem ineffective. We've not been on the end of the bullying you speak off, but I know the school's dealings with it can be hit and miss from my daughters, friend's, parents. A lot of the time things are white washed over, 'nothing to see here and let's all be jolly good mates again girls'.... it's very old school. needless to say the issue usually persists.
The academics are good, your daughter will have plenty of constructive stuff to get on with and wl do well, but there's an underlying air of competitiveness that feels slightly unhealthy in today's age of mental health, and although sport is well provisioned, in lovely settings, we've found that once you pick something extracurricular you cant change it even if you're either (A) bored or even (B) feel its clashing with your studies. It's all quite odd!
On the slightly less academic flip side, DD has a good friend at Tormead who's in her scout group, she seems very content and tormead has definitely got a more modern style/feel to it than the 'tradition' you'll get at st cats. It's all personal preference.
I think in summary, unlike when we chose for our DD all those years ago, if we were to repeat the same exercise now, Tormead would definitely be in the running as a v strong contender.