I'm so sorry, Tilly - I didn't mean to offend you. I think people in all sectors are often inclined to leave it to the school to sort out problems, and it's often difficult to intervene, actually; schools don't always encourage it. But evidently that wasn't your problem. I just think perhaps we're all urging you to focus on solving the GCSE problem/s, rather than issues about fees.
How big is the gap between their grades and their mocks marks? This is obviously the point to make, because what you now need to do is to focus on getting them extra help - form the subject teachers concerned, and if necessary from outside. My sense is that you'll be more likely to succeed if fees aren't a big part of the conversation.
As to your question about university fees - there are all kinds of problems here. If a poor grade means a fee refund then the result will very simply be grade inflation.
If poor teaching is concerned, what does this mean? Does it mean, 'whoah, that's waaaay less time than somebody at another university got' or 'that is way less time with someone with tenure as opposed to a postgraduate' or 'I didn't understand a word s/he said', then who is to adjudicate about this?
My bet is that lots of teaching in every sector is poor, but - sorry - students are not always good judges; what they very often like is a handout with bullet points that they can plug directly into a term paper, and this isn't always the best way of developing intellectually. You actually have to pry their anxious fingers off you and let them go it alone a bit... and if all doe snot go well this can be interpreted as failed teaching provision.
You could ask the same kinds of questions about GCSEs, I think. Maybe your dcs were if anything too well supported, hence floundering in mocks and not realising it was ultimately down to them to revise and practice?
Hope this helps. I mean it to help!