This is what "I" would do.
Make a presentation to your parents about homeschool versus the school you go to now.
#1. They would/should be impressed on how much work/time you put into the presentation and
#2. You'd have a lot of info. for them to look at that would hopefully strengthen your presentation.
There are TONS of websites that you can check into inregards to online homeschooling. Just do the research and go online with the search as "online homeschool programs."
Here are just a couple of suggested sites:
I don't think that you are going to find much on the 'FREE' side, but give these a checkout and see if it helps.
Good luck to you kiddo.
BTW I "LOVE" the UK. I've been several times and have absolutely tons of relatives there. My Mum is English (Sunderland).
Anyway, good luck.