You may already have seen this, but
here is the BGS autumn list of extracurricular clubs. In the summer cricket (& tennis to a lesser extent) would replace rugby, football & netball. My boys never played hockey in 7 years at BGS (they may have done in lessons!) and I've never seen any mention of a hockey club.
In a mixed school there is, of course, a much smaller pool of boys or girls to choose from for teams. This could either mean it's easier to get a place in a team, or that there are fewer teams for each sport.
I know that cricket is very popular at John Hampden, and they run a summer tour to Sri Lanka (or certainly have done in the past). BGS runs a rugby & netball tour to New Zealnad evry couple of years.