Phil.. You absolutely will not be discriminated against. I knew some very good ATCOs who had several degrees. However, IMHO, like other experienced controllers have suggested, graduates do not necessarily make good ATCOs otherwise a degree would be a requirement for candidates. Educational qualifications are not the be-all-and-end-all. Some have lots; others don't. I have 2 GCE O levels but I worked alongside people with 8 O levels, 4 A levels, various degrees and other qualifications. All of us were better than some, not as good as others doing the same job. But we all had the same quirk for doing the job.
Some people can do ATC whilst others cannot and I've yet to be convinced of any test which claims to pick out those who will succeed!