I really would advise against putting your child into a school you can't yet afford at this stage.
You have no guarantee regards your future earnings and I am afraid Barristers, although may earn an very good living, are not guaranteed a high income, and as a newly self employed barristers you may fnd getting loans, etc difficult at that time too if you find yourself still struggling.
School fees raise greatly each year, by as much as 10% a year. Uniform can really add up, even from pre prep years. Then you will need to factor in child care costs - private schools have longer holidays than the state secotr, and many holiday clubs, if the school doesn't offer it, will not take these extra weeks into account. Then there will be the extras - like you get in state school - so clubs, trips away, etc.that on top of fees, ay be just enough to push you over the edge.
If you can't afford the school now, then netxt year is going to be even more difficult, and so on. It isn't worth the amount of stress this will cause, believe me. You will have enough on with the training and pupilages as you become a barrister.
Do some more research into the schools around you. Get your name on the waiting list for the school you did not get into, and keep checking on your status on that list. Sorry, not what you want to hear, but I don't see how you can send your child to a school you simply can't afford.