the school have told me that if there's enough bursaries available
IF
we'd be eligible for 100% plus if you have a sibling already there then you get priority
IF
If your financial circumstances change then you need to let them know and they'll re-assess, but obviously if our finances improve then we'll be able to afford more,
IF - but you're not able to afford that "more" right now. You have help for two years.
so when our daughter leaves we'd be able to pay more towards our younger child's fees.
If your second child gets in on a 100% bursary (very optimistic) when your first leaves, that will probably be reduced to 50%. And even without a Labour government, that will be 50% of more than it is now, because fees rise annually.
Plus your first will presumably be in uni which you'll be expected to financially support her for. That's MASSIVE outgoings.
Please understand that private schools do not work in the way state schools do. This is a selective school. It trades on grades. Your child has something they want. They're offering part of what you do. The deal right now isn't in your favour. They've got you bedazzled because you feel special. That's how this works. Move past the feelings and look at the numbers in black and white. Then negotiate. This is business.
Also, you're forgoing financial security and opportunities for your younger child if you accept this deal too. She's not going to be in the "good" school and she'll have no nice new things or holidays. If you can't afford the deal offered to her if she passes the entrance exam, she'll very likely end up resentful that everything went to her sister. There's more to this situation than a bursary that's not enough.