It is certainly possible to self-study, although requires a lot of effort on your part – especially if you’ll be aiming for top grades.
Firstly, you’ll need to discuss this over with your Head of Sixth Form and see what they say. Your school/college will be used as the examining centre, so this shouldn’t cause any complications.
Secondly, go over the syllabi for each subject from the different exam boards. Generally speaking, the same things are covered, although there are occasional differences, and of course the style of exam paper can differ greatly.
After you’ve done this, you’ll need to purchase the relevant books and get your head down. Don’t forget there are also plenty of websites available which can help, and of course TSR can be an invaluable resource.
If you’re contemplating Further Maths, then I’d highly recommend contacting the Further Maths Network. It’s an organisation which is there to help those take Further Maths even though their school/college may not have all the necessary resources.