A degree may well be an advantage in the search for a sponsorship, or a flying job, but it is not usually a requirement - in UK. There have been some employers who have expressed a strong preference for degree-qualified candidates, and one or two sponsorships in the past have required a degree, but they are in the minority.
There is little or no relative advantage, in employment terms, for a prospective pilot taking an aviation-related degree. Where a degree is preferred by an employer, it is the fact that you have studied for, and succeeded in achieving, a degree that is important, rather than the subject. This is not a similar situation to engineers, lawyers and medics, for whom the degree is an integral part of their professional qualification process.
Therefore, the degree you choose should be in the subject you enjoy most. If that's aeronautical engineering, great, but don't expect any more credit for it than the guy who did history.
As for the more practical aspects of getting into flying, as Chuffer says, get in an aeroplane and see if you like it. Have a look at the study required for the ground exams, and be sure that you're ready to take that on as well as (or soon after) your degree. Get a Class 1 medical. If there are any issues which may prevent you from getting one, deal with them now. DO NOT spend any money on professional flying training until your Class 1 is in the bag. Do the GAPAN aptitude tests to assess what your potential is (do a search in this forum if you've never heard of the GAPAN tests), and think carefully about the wisdom of committing serious money to training if their advice is against it.
Work hard. Be committed to your ambition. But above all, enjoy it!
Scroggs