Given the position you're in, my advice would be to take a year out after you finish your A-Levels, continue living at home, and spend a year as a social worker to see if you really like it. In the meantime, you can apply to universities in the Sept 2026 application season, where it sounds like you might have a strong application on your hands (if your predicted grades are correct). You should definitely also have enough content for a good personal statement, since your achievements in UKMT / Kangaroo are ridiculously impressive.
I was in a similar position to you in year 13. I had received a post-school job offer which I was keen to take as a full time role, but my parents thought I should go and study engineering at university. I decided to wait it out, and managed to achieve A*A*A*A* at A level (in maths, further maths, physics and english literature). I took a gap year and decided to commit full-time to the job i had been offered - in the meantime I applied to universities through UCAS. I received offers from top unis, and I realised that universities love applicants with strong achieved grades, rather than predicted grades (it is a much better indicator of your actual ability, since most schools inflate their students' predicted grades). With my A-levels and a decent personal statement, I received an offer from the University of Cambridge to study engineering, which I was surprised by. I continued working and then finally decided to take the offer from Cambridge come the end of my gap year. This was a route which worked for me. I was able to save up a significant amount through working during my gap year, get a student loan to cover the rest, and then head off to university. I am now in my 2nd year applying for jobs and internships, which has made me realise that a degree is very important for higher paying jobs. A STEM degree (like mathematics) would put you in very good stead for many jobs. There are certain roles such as quant finance which offer ridiculous salaries (~£300k+ in the UK), and their main source of graduates tend to be mathematicians - especially those from top unis and those who have achieved highly in competitions such as UKMT and kangaroo. Many of these high-paying roles are (unfortunately) very male-dominated at the moment, and so firms have lots of programmes aimed at recruiting keen female applicants. Given your abilities, this will put you in an even more advantageous position if you do decide to go for some of these jobs later down the line. Another suggestion might be to study a vocational degree (that is, one which directly leads on to a career). You are clearly very smart and good with numbers, so engineering might not be a bad suggestion?
My overall advice would be this: don't let your natural talents go to waste. Take a gap year, do some social work, and apply to unis for maths (or a maths-related degree) in the meantime. If you get an offer from a top uni definitely take it! I wouldn't necessarily recommend just applying to your "nearest one" - it sounds like you are very capable of applying to the top UK unis such as Oxford, Cambridge, Imperial, etc, and these are considered "target universities" by a lot of employers. If you don't end up getting offers, you can always continue your job as a social worker and see where life takes you. All the best - Good luck!