There are a lot of private therapists and a lot of different therapies so choosing one can be a minefield. I always recommend contacting a few people and seeing if you like their response. Therapists are just people so it’s important that you feel you would get on with them. You can give a few details about the work you want to do, ask if they have experience in that area, ask if they are a member of a professional body, and find out about appointment times and prices.
These two directory websites also have good information on how to choose a therapist:
https://www.bacp.co.uk/about-therapy/how-to-find-a-therapist/
https://www.counselling-directory.org.uk/memberarticles/how-to-choose-a-counsellorpsychotherapist