OP I’m so sorry. You sounds utterly distraught.
I’ve been in your position and I know how badly you feel you have let your children down. It’s not about the money is it, it’s because it’s our job as parents to provide stability and school is a large part of our children's lives.
The children will find this hard but they will be okay. You need a game plan and you need one fast. You’re going to have to do all your crying in private. I know how that goes too.
I would suggest writing to the bursar asking for some leeway with notice. We did this and managed to get a January release date following October notice. You also have a bargaining chip - move your older child at Xmas if you can, using your elder child’s notice on top of younger, aiming to move youngest at Easter at the latest.
go in negotiating hard. Yes, the school is a business but they hate hearing about our personal finances. Be brutally honest & use terms like ‘no more money’ ‘cannot afford it’ etc. be very basic and explain that a full term notice is not going to be happening. They are very very unlikely to sue you. Truly.
remember as well you may have a deposit to be returned. If the deposit is £500 - let it go. Your fee saving will be more. If it’s a terms feels, negotiate with them.
I’m so sorry this is happening. You must be feeling sick and it’s a terrible shock. None of us want to uproot our children. You can cry in private but in front of them, get a grip. Be honest with them about finances. Don’t frighten them but be honest. Let them be honest with their friends too.
lots of love.