Hi Gaz,
I'd suggest going for the Masters, getting a few hours light aircraft in your spare time and going for the FPP while working through it. BA will be looking for a bit of maturity and experience as each MPL has a different type of person in mind. If you've got extra skills that have the potential to make you a specialist Pilot in future (Tech pilot/management Pilot/Safety Officer etc.) then that stands out as well. So many skilled people go for these positions, you need to bring more to the table than anyone else! A Msc would help there.
Also, if it doesn't work out then you have a solid fall back and career options to tide you over to the next intake and so on. Just make sure that you love what you're doing and best of luck!