Hi jk2212,
I was in the exact same situation as you last year (sat the May 2015 session and resat in the November 2015 session), missed my offer from Kings due to Physics HL so I decided to re-sit the paper in the November Session. It is absolutely possible for you to do this, however you must have everything prepared and your UCAS profile set up and filled in (apart from the resit grades) before you even get your IB results. I had about a week between receiving my IB results and sending off my IB application so you gotta be organized in order to not miss the deadline (mainly due to uncertainty in which uni to apply to).
Before you make the decision to pretty much take a gap year in order to re-sit some exams you have to make sure that the university/course accepts applicants with resits or applicants with grades form 2 different exam sessions (Durham and King's accepted my 2016 entry UCAS application and am currently holding an unconditional from Durham, however i'm unsure about UCL though). If you do get accepted into your reserve choice uni but still want to do this, you will have to reject their offer in order to open up an application on UCAS 2017.
Also very important to check is if your school will provide support or resources for your re-sit, especially since you are planning to potentially resit 4 subject (2 of them being maths and physics HL) and get 7's, if you don't get school support seek out a tuition centre as it will be very difficult to prepare for all 4 subjects alone.
And a personal word of advice, find something else to do during the gap year to improve your Personal Statement or else when you apply the uni's will wonder what you have done for the rest of your gap year, I personally chose an internship to compliment my business/economics orientated application.
If you have any other questions regarding the procedure or my experience doing this please do let me know.
**Deadline for signing-up for November session is July 28, after this sign-up costs increase