Can I just add in that my children are educated bilingually in Scotland (English/Ghaidhlig - Scottish Gaelic, state school provision) and they start a 3rd language (French) in Primary 6 (year 5) and a fourth (German or Spanish) in first year of secondary (y7).
Many children, mine included, at primary level are learning another language outside of school - mine are doing Spanish and storming ahead at eqv y1, 2, 4.
The Gaelic system in Scotland (like Welsh in Wales as far as I know) uses a total immersion system for early primary even if the children don't have the language at home. I now have 3 children who are Ghaidhlig "native speakers" even though my husband and I have none. It amazing hearing them insulting each other over the Wii in another language!
For littlies, in my experience the "total immersion" to begin with is really important. In my children's school everyone - teachers, office staff, classroom assistants, Janitor, lunch supervisors (not the dinner ladies though) speaks only Gaelic to the children on all occasions unless they are actively teaching them English (which they begin to learn to read/write in the middle of p3 - Y2).
If you are looking at setting something like this up in London for another language, you could do a lot worse than make a visit to one of the Gaelic schools in Scotland - we're at Sgoil Ghaidhlig Ghlaschu - Glasgow Gaelic School, which is the most developed, although there is also one in Edinburgh.
I understand that your school will have to be private and fee-paying, and with that you will have to go along with the preferences of the parents in order to attract students. But the Scottish/Welsh bilingual schools have been set up as state provision so are much more free from that kind of pressure and they are doing what really works academically for young children in a bilingual setting and it might be worthwhile you looking at them, if only for advice/support.