Hi Danni. Sorry you don't have a precise diagnosis, that must make life difficult. The bulk of diagnoses are actually made by GP's. They are pretty good if you only suffer from one disorder and your symptoms are classical for a particular disorder. They have been known to struggle with more complex situations. It sounds like your situation might fall into that category.
Greater complexity generally means accessing a psychiatrist. They can be found in various locations. My Community Mental Health Team has one. My Crisis Team has four. Psychiatric out patients has any number but they each cover a particular geographical area. None of them will see you off the street, you need a referral from someone, most often your GP.
In your situation I think I would see my GP and ask if they felt capable of firming up your diagnosis. They may not feel able to do this. In that case they can easily refer you on. I have seen out patient psychiatrists often and CMHT's a couple of times. In terms of diagnosis, both were about equal. If you are thinking about treatment and support afterwards I would say CMHT's have quicker access to a range of services. My team can supply CPN's, Support Workers, OT's, Clinical Psychologists, Social Workers, Counselling, and Psychiatry from their own resources. They don't need to refer on.
Anyway I hope you get somewhere. As an aside, the Citizens Advice Bureau can be amazingly good with money matters.