Which of the oldline, posh, all-girls' boarding schools in England still has mostly British students?

Many of these old elite boarding schools are now overrun by the daughters of extremely wealthy foreigners, leaving little space available for native British girls. Rodean, for instance, now has almost as many Chinese nationals as British girls. Cheltenham Ladies College is another example of how these schools are now recruiting foreign money over British students. Are any of these old line independent boarding schools for girls still largely British in their student body makeup?