There was a second girl's boarding school based at Down House from 1924 to 1927 but then it closed. Trivia: I was at a prep school about a mile from the present Downe House School between the ages of 10 and 12. We attended concerts there, but otherwise had no contact with those strange mythical beasts called girls!
If anyone is planning a visit to Down House, the car park is some distance from the house, but there is a decent footpath suitable for a mobility scooter between the two. If you have a blue badge you can park actually at the house, space permitting. Disabled visitors who need a scooters or chair will need them for the "long walk" down towards the glasshouse. HTH. Oh, and of course it is closed at the moment.