The fastest possible and best way in my opinion is to get into a sixth form and start doing A Levels, if you would like to go through this route, start by contacting your local sixth forms and discuss if anything can be done. Most sixth forms would've required a certain GCSE grade prior but some may be able to make an exemption or offer alternative arrangements considering your situation.
If none are possible, you probably should take the GCSE exams before applying for sixth forms. Have a look at the GCSE specifications for different exam boards for the compulsory subjects and see if you will be able to take the exams in the next exam season (Summer 2023). When you do feel confident and think you can take the exams, contact local exam centres (mainly schools, sixth forms, and colleges) to see if you will be able to take the exams as a private candidate, this may come at a cost. Please do this as quickly as possible as there may be deadlines as to when you can apply. Since you would not be studying in a school, you will not be able produce reliable predicted grades, thus you will need to apply to sixth forms to study their A Level courses after you received your results in August, as a late candidate.
You can also try directly applying as a private candidate for the A Level subjects, for the closest exam season (Summer 2023) if you are confident, but it is known for its difficulty so please do try some past papers before doing so. Then apply to university through UCAS when you receive your grades. Again, you do not have a reliable person to produce your predicted grades and reference if you go down this route so you may need to apply through clearing after the A Levels results day and can apply for some jobs and ask managers to write your reference.
Best of luck in doing this, this journey sure sounds like a tough one but you will definitely make it. If you do have any more questions please feel free to ask and I also want to see how you progress here
Private candidate information:
https://thecommunityschools.co.uk/articles/how-to-book-an-exam-as-a-private-candidate/