If you’re looking for a psychologist, the only real way without going private would be to go via the NHS but the wait times are long. I was actively suicidal and self harming and was told there was a 2 year wait before I would be able to be seen. Psychologists working with the NHS don’t always necessarily offer proper therapy either. It sounds as though you may benefit from longer term therapy and within the NHS it tends to be time limited. Private psychologists are expensive but you may benefit from a different type of psychotherapy. I have had person centred therapy and you’re right, it doesn’t dig deep enough to come anywhere close to dealing with all of my issues from the past. It works well for some, but just not suitable for me. Before lockdown I began seeing a psychodynamic therapist and within the first couple of sessions I felt a completely different sense of therapy, one that I knew would get to the route of the problem. This would be a much more affordable option for you than a psychologist, lots of private Ts across the UK use a psychodynamic approach. The BACP list of counsellors is a good place to start looking as is the uk counselling directory. There are also some centres that offer therapy at a reduced rate for those that struggle to afford it. For example I know of a centre near me that offers open ended psychodynamic therapy and after the initial assessment fee (I think it’s £25), you pay what you can afford per session.
Good luck finding someone.