I'd look on UKCP as I think their registration is a bit more rigorous than BACP.
Then is look at practicalities (how far away are they, can you afford what they charge, do you want face to face or online therapy etc).
It is hard to know what type of therapy will suit you before you have tried it but you could have a think about what you might relate better to. Do you want someone who is neutral towards you or someone who shares a bit more of themselves as a person. I would suggest CBT might not be the best fit for you as imo it deals more with the symptoms of trauma ( how to manage anxiety etc) rather than root causes ( eg traumatic relationships in childhood). I didn't find it helpful as I needed to address root causes.
Look for people who may have experience/specialisations in childhood trauma/relational trauma.
Then make a shortlist of 3-5 therapists based on your investigations above and contact them. It may be that they don't all have space at the moment.
Of those that do, arrange an initial meeting/phone conversation or whatever they offer. Some offer a free 30 minutes or a reduced price first session. Some charge full price for an introduction session but don't be put off by that.
In the session, explain a little about how your childhood has impacted you and ask them how they would approach this with a client.
Then go by feel/ gut reaction. Is there a therapist you felt you clicked with better? Arrange to start with that one. After about 4 -6 sessions evaluate what you think. It usually takes at least that long to get a real sense of how things might work with a therapist. If you aren't certain that things are going well, discuss openly with the therapist and explain how you are feeling. If you still don't feel it it is a good fit stop therapy and try one of the others you identified - maybe one that has a different modality than the first one you tried.
It may well be that the first therapist you start with is a good fit but don't be afraid to try someone different if need be
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