Stickman
There are a number of references to the Martineau school in the index to "A Breath of Fresh Air : Birmingham's Open-air Schools, 1911-70.". I don't have the book, so can't say if it gives the information you want. The book "A history of bognor Regis" by Gerard Young is not clear, but says that, when the house was demolished in 1932, the whole estate became ripe for development and was comprehensively redeveloped. While it would seem that the school would have been on the site of the estate, I would have thought that, if the school was on the site of the house then that would have been mentioned. Looking at the online index to the west suusex archives, i was surprised that the only mention of craigwell was a letter from the shippams archives from the king's chef, presumably praising their calves foot jelly, which, I remember from my youth, was always pushed for invalids by the firm
mike