A Level Resits as a Private Candidate (Fees, Centres, etc)

Hello, I am on a gap year and just finished my A Levels this summer. My grades were far from what I expected but thankfully my first choice was lenient and gave me my offer (I applied for deferred entry). However, since I am taking a gap year, I want to keep myself updated with the content (maths, physics) so I can have a smooth transition to uni September 2026.
I am planning on resitting two of my a levels (AQA and Edexcel) as a private candidate and am looking for affordable / free resit exam centres. I know that I can retake in my old school, but I was on an academic scholarship at a private school so 1. I would have to at least pay £400 or possibly they won't even let me resit as my tuition was covered for 2 years only 2. I'm a little embarrassed as I was on a scholarship + they make resit candidates sit at the opposite end of the hall.
So I took a look at all of the private exam centres in London (I am only looking to resit the exams, not study them again), but I found that they were so expensive + scammy? For example, Edexcel themselves only charge around £120 for all of Further Maths, but I've seen centre charge an extra £200 per paper just for taking the exam there. That's £920 just for one subject, surely this shouldn't be normal? Anyhow, I would like some suggestions on what local colleges would take external private candidates for an affordable fee / even free?
I know that for state schools / sixth form colleges, all exams are free for the students because they're funded by the government. I am 18 and my household income is quite average / low (I was on a full-ride scholarship previously), so maybe there's a chance they could take in someone like me??
If you're in a similar situation / general gap year student, feel free to connect w your experiences!! Sorry for the long rambling guys & thank you for reading