Couple of things.
Firstly, if you are talking about not starting flight training for 10+ years your comments about BA Cadet training are mute. Noone knows what the world will be like in 10 years time.
Integrated at the moment you will probably need £100K. If you are starting from scratch money wise, each year in Uni is going to cost at least £8K so when you start working you will be paying off student loan. Also the tax man gets about half your income, plus you need to live... On your plan - you are still going to be quite short on cash.
Flight training in the USA is cheaper and there are many more jobs available. I don't know about sponsored programmes, but if you are happy to work over there then I believe there are more opportunities.
Switching between a UK JAR / EASA licence to an American FAA licence isn't that easy although it is possible.
Keeping looking through the options though! Unfortunately there is no easy/ cheap way of becoming a pilot, unless you go through the military (and they are cutting back on pilots).