When you say "next to nothing left over" OP, do you mean after all bills, mortgage, food, basic clothes, transport etc are paid?
In other words that normally you either save £20k a year, or spend that much on unnecessary things like holidays and meals out (or a combination of the two, obviously)?
If that's the case, then I guess you can afford it, as long as nobody minds not going on holiday or any of the other nice things.
Bit miserable if you ask me tho.
Remember that secondary is a much bigger pool than primary, and most kids will find their tribe, whether that is nerdy techy kids, smart bookish types, gamers, actors, singers, musicians, footballers - I could go on. I taught in a deeply non-fancy secondary and there were friendship groups for all those and more.