ShaneJ
I must admit I love your enthusiasm. You will go far.
I self taught myself A-level mathematics concurrently with commencing study for a mathematics degree with the Open University. It is perfectly doable with availability of time, and lots of application.
However, looking at the A-levels you are starting I feel you would find it a bit tight. There would be a risk that your school-arranged A-levels, your mathematics A-level, and your Open University studies would suffer overall and you wouldn't do yourself justice in any one subject or study route. I would therefore advise the following, in this order:
Firstly, ignore your school's intransigence and register to take GCSE mathematics as an external candidate. If you look at the AQA website, you will find a list of centres that specifically take external candidates across the country. There are lots and there will be one close to you. I would register, in due course, to take this next summer.
Secondly, continue your mathematics A-level studies by yourself with a view to taking the AS level units externally next summer. If you obtain good passes in both GCSE maths and AS level maths, I find it difficult to imagine your school will not allow you to take A2 with them, with a view to going on to do mathematics at university.
Thirdly, if your school won't let you do A2 maths with them after getting good GCSE and AS maths results next summer, then study A2 by yourself... and or move school. You don't have to stay studying where you are.
And then move on to university studies with the OU or elsewhere. Meanwhile, and to enrich your mathematics study, and if you have time, consider getting the Open University courses MST121 and then MS221 from Ebay. The full course material comes up for sale regularly and you should be able to get them for around £50 each. I did this for both courses prior to formal enrolment. Compared with the full current cost of around £1200 each, that is somewhat of a bargain and you can sell them on again to recoup costs. They are great courses and fully self-studyable.
Really good luck with this. Fortune favours the brave!