If you have a care coordinator (be it a social worker, CPN or qualified therapist), ask about the possibility of being referred to your local personality disorders team. These are usually the people best placed to offer a diagnosis. You may also need the backing of your consultant (usually the care coordinator acts as an intermediary) so i'm hoping you're on good terms with them also.
It took me nearly a year to beg to be referred to the PD team, once it was agreed i spent 10 weeks in assessment and once i was given the diagnosis i started DBT.
All i would say is do your research - and don't take no for an answer. If necessary, refer to the NICE guidelines and/or get involved with an advocacy agency who can speak on your behalf in appointments etc.
It appears you're already part of the social group i created for members who need support and guidance on UK mental health services. I encourage you to check back in with us for further support and to access some of the links listed there.
Very best of luck to you Fuzzybear