I would ask for a referral to a good DBT therapist. It has been proven clinically that it is an effective treatment for this disorder.

Well apart from a referral for which I would have to go to my GP to get, what sort of discussion could I have with my counsellor.

Have you done research on the diagnosis? I would say that it's best to work with someone who is very familiar with it.

As one of the traits is fear of abandonment and rejection, I am afraid my counsellor will say "i don't know anything about this, goodbye"

Abandonment is one of my "issues"

scars,

I think psychoanalysts are safest as they are trained specifically for attachment issues, especially transference. bpd is primarily from attachment failure, imo. i have those issues too. I only feel safe with analysts and not other Ts because they are required to do depth therapy for years and be fit to be therapists. I don't know other types of therapists who get that litmus test. although some other types of Ts have done/do that type of work. just fyi

DBT might be better for some both for personal preference or due to ego strengths. aside from personal preferences, people who are not as 'high functioning' might do better with DBT.

good luck