I suspect he doesn't actually do it, because at that level of school, one of the products parents are buying is the transition of their child to a decent university, if he does anything to hamper that most will take the £34,500 and their offspring elsewhere. It may be that he has several parents who don't want their child to have a relationship in case it messes up their school work which might mess up their university application which would mess up many of those parents projected path for their teen. I am sure someone can come along and defend the school but I am not sure that he is the sort of person I would want directing my child's time at school
It's a co-ed boarding school. Thus any underage sex etc during term time will happen whilst he's responsible for their welfare. Thus I imagine a need to take a harder line (use scare tactics etc) than your average day school, at which (generally) pupils even if they're having underage sex, are unlikely to be having sex whilst the teachers are actually responsible for the pupils.
(Though of course if they're kicking out students for showing interest in anything beyond their studies their results probably say more about their selection of pupils who are going to do well as they do quality of teaching)