Emily you certainly seem to have got your head screwed on. Bags of common-sense which regretfully isn't very common.
An excellent & logical plan and represents the least risk approach.
As an instructor with the ATC I recommend you join NOW and get involved in all squadron activities, get noticed for the right reasons. You will find that the academic side of the Corps is a good grounding for the PPL. The Corps also offers various gliding and flying scholarships (subject to selection).
Joining the ATC not only does it show your interest in flying; it also shows leadership potential to future employers.
The only thing I would suggest is that PRIOR to starting your PPL go down to Gatwick and get a Class One Medical as you need it eventually for ATPL/CPL.
Class Two okay for PPL training but you must look beyond.
Best of luck and please PM me for any further advice if you wish.