Certainly the military path is the 'normal' route to the TP world, especially in the UK (almost without exception). There are more RAF TPs than RN or Army TPs... take that as you will (there are, after all, more RAF pilots than RN or Army pilots).
The engineering degree route will certainly help (although it is not a pre-requisite) and the UAS world is a fine place to start a miltary flying career, IMHO.
I remember going to my UAS interview and stating that I was interested in becoming a TP... it was knocked by one of the QFIs on the panel. I ignored his knocking - haven't looked back since. It is a fascintating area in which to work, if it suits the individual. It is ceratinly not the 'Right Stuff' world of jumping into your hot pursuit ship and blasting off to set a new airspeed record (not in this country at least) but, for those with a genuine interest in aircraft and why they work (and sometimes don't), allied to a fair degree of intellectual curiosity and tenacity, it is a fine career (or vocation).
My advice would be to keep your options as open for as long as possible and see where life takes you. If you end up in the military and are still interested, then go for it!
Good luck, whichever way you go.