...although a degree will be very nice for you - any employer that needs a licence will get a licenced guy first. A degree is not much use (an implication, there, of some use) on a Line or in a hangar.
Degrees are mainly the need of design, possibly management positions or manufacturing/production.
Depending on what degree it is: a degree may not help in the exams you will need to pass for a licence.
Recently degree qualified and licenced guys (straight out of civil training) have been noticed as a bit better at fault finding, but not that different.
In the mean-time:
Keep an eye out for Engineers Licence Guidance Document (ELGD) on the CAA.co.uk "publications" webpage - it may re-appear soon.