You need to make yourself a valuable customer.
At the moment, they see you are very interested in flying with them and don't want to go elsewhere. That puts you at a disadvantage.
If you go in there and tell them you will be paying monthly or 'pay as you go' and tell them to take it or leave it. Once you walk out of that door, the deal is off and you won't be taking lessons with them. If that happens, they've just lost £8k due to a fault of their own. £8k is just the start. Your lifetime value for the flying school is huge. You're only 15 so think how much money they can get from you during your lifetime, though lessons, plane hire, cafe, recommendations etc.
If they accept then you can be happy!