Everyone who is BACP accredited will be fully qualified with a lot of practising hours under their belts so that is a good place to start.
I've always felt, and have been told by many professionals I've been involved with, that it's not the approach or the specific training (although you obviously need to feel comfortable that they have appropriate qualifications and experience) that determines the effectiveness of therapy. I absolutely believe that whether or not therapy is effective comes down to the relationship between you and the therapist. They can have all the qualifications in the world, but if the relationship isn't there or isn't genuine it pretty much means nothing.
I realise that's not at all helpful for your situation. Finding a therapist is tricky, if you feel able to I would suggest that you call a number of people listed on the BACP website who you feel might be appropriate and see how you feel about them from the conversation you have. Tell them what you want out of your sessions and if you think it's worth looking into further, arrange to see them for an initial session (which should be free) and go from there.
I see a private therapist but I didn't have to go through the process of finding her myself. I started out seeing her nearly 10 years ago at one of those young people's drop-in places that offered counselling for free as a charitable organisation. When she left there, she took me on as a private client.
Only other places I can think that might have a list of therapists in your area is your local Mind or Rethink branch if you have one? They have a lot of information so they may be able to help, and
www.cpdirectory.com is another website.