@AFistfulofDolores1 it's good to hear someone talk about their experience with analysis/ psychoanalytic psychotherapy.
As others have said as psychotherapist isn't a protected term, anyone can say they are a therapist. So it is really hard to navigate finding someone properly trained.
If interested in the analytic way of working (understanding the unconscious and impact of early experiences and relationships) which is not for everyone, but very significant for many, it is a very intensive and often longer term process - although not always. Then rather than looking for bacp therapists, a more specialist accrediting body would be the bpc (British Psychoanalytic Council) and for children and young people (doctoral level)- the Acp (Association of Child Psychotherapists). These trainings take years, many therapists/ analysts train (particularly the child and adolescent ones) in the nhs and go on to work there, as well as sometimes privately.
But, I know that getting this kind of treatment on the nhs is not easy and depends where you live.
There are some really good low fee schemes available too in some of the adult training institutions.
Clinical psychologists do have a protected title, so people cannot say they are a clinical psychologist unless they are! They have also been trained in the nhs until doctoral level and have a broader training in different areas and modalities- so not as in depth as the psychoanalytically trained above, but may be able to work flexibly eg- cbt or emdr, systemic etc
Other trainings and ways of working may be really helpful for different people- there are lots of good people out there. The difficulty is knowing who and what. Some people do brief trainings in cbt, or emdr etc and may be fine/good at doing those as interventions.
Others do counselling or psychotherapy trainings that, a bit like psychology, include different things. Again, they may be great and some training courses are obviously better than others. But I do think its a real problem that none if it is well enough regulated and as above anyone can say they are a therapist or counsellor.
I know this doesn't really address your op but, given the way the conversation has gone, thought it might be helpful.