For sure the Magic Circle would prefer the York non-law and then GDL. Sorry but come on, Man Met will never cut it for a MC firm. To start most would people mock you in saying "oh, you weren't clever enough to go to the University of Manchester", which for starters is Russell Group like York, respected, and a fair few graduates from there end up at MC or city firms as per the link below. If you scour Linkedin too that will also show this, especially recent graduates.
http://www.chambersstudent.co.uk/media/1067/what_is_a_good_university.pdfMC firms love the Russell Group and Oxbridge, and as others have said, scour their trainee intake from the past few years and you'll see what they mean. You'll find very few non RG graduates, and those that are, are from much better unis than Man Met. I'd say the best non RG for the MC is Leicester. Any lower than that, not a chance.
Finally, your A levels are not good enough for the MC, because most MC firms and the city firms have filters of AAB, some ABB. You have ABCC, which is pretty poor for applying to a MC or City firm. Regional firms and lower; yes you have a chance. It does not matter even if you magically ended up at York cause the catch is your A level grades, so then its not your uni that lets you down, but your prior grades. The filters are usually at the very beginning of an application form asking do you have AAB/ABB at A level, and if you do not have the grades, thats you gone. No application possible.
Sounds harsh but stop kidding yourself, I'm afraid you wont be the next Harvey Specter raking it in at an MC firm.