Please explain if I would be able to do this and if it has been done before?

I want to retake my A-levels but don’t want to resit Year 13 or pay for a very expensive private centre.

So, please explain if I can do this:

Can I teach myself independently for the year and then go back to my old school and sit the exams there in the summer? I know I’ll have to pay some money for exam entry fees but they may give me a discount as I am a former student unlike the extremely costly private test centres.

Is this doable?

If you old school accepts private candidates, and if you won't be enrolled there are a student (i.e. being taught there, even for another subject) then yes, this is a viable option.
Whether or not they'll be able to give you a discount on the exam fees is another question!

I’m not sure if they accept private candidates because when I sat my exams I didn’t see any strangers.

However, when I sat my A-levels, I saw a Year 12 girl retaking her Biology GCSE. Would she be considered a “private candidate” as she would have been paying to sit that, especially since Biology isn’t a core subject like English or Maths but she was doing A-level Biology lessons (not GCSE Biology lessons)?

Also, I’m just curious but I’m eligible for a bursary. If I retake my A-levels privately, can I still claim a bursary or can I use the bursary money I would have received if I returned to school to pay towards my exams?