OK, the book you need (with a possible answer) is 'St John's Wood and Maida Vale Past', by Richard Tames, published by Historical Publications. I don't have this in my collection I'm afraid.

I've checked my copy of Old and New London, and there's no mention there of Barrow Hill School. I've checked a few other 'encyclopedias' of London that I have here - about 15 different ones - and the only mention I've found was passing reference to Barrow Hill as being close to Primrose Hill (in an article about the Metropolitan Water Board!)

Even a web search drew a blank. Sorry I couldn't be more help.