Hi Alan,
Depends on what you would prefer. B1 Licence is airframe and engines and some avionics. B2 licence is your real avionics including radios, radar etc. These licenses are what are used throughout europe and reconised throughout the world.
With your degree you would be exempt from a few modules which I think in your case would be maths and physics but YES you would still have to complete the B1,B2 course requirements.
I suggest some reading on the CAA website, under personal licensing, then under engineering and that will give you the exact list of what the feds! {CAA} want you to do.
Once you have the license, you then have to undergo work experience to gain the relevant experience. This is paid work but without any experience your no doubt be the apprentice in some ways.
But it is good fun and its a brilliant job when you get with a good company.
Good luck
c24