@Decoupage , I'm wondering about what issues brought you towards seeking a therapist (not that you under any obligation to share these, of course), because to me it seems quite striking, even surprising, that you have found the therapy invaluable each time. I'm well into my second year of weekly NHS psychotherapy (with a good therapist whom I respect a lot) and have yet to experience any kind of breakthrough, though I find the sessions very supportive.
I suspect that the reality for very many people is that the mental health support they receive, if they seek it, is relatively marginal - something that they can't decisively say was worth the investment of time and in some cases money. That uncertainty of benefit is one barrier.
I'd also like to second those who say that it is hard to find a therapist. When waiting for NHS treatment I did my research into private therapists, picked one, and she was just so dreadful, so lacking in any disciplined or focused approach that I thought that the business of finding a therapist was as hopeless as looking for a fossil among all the pebbles in the beach. So I stopped.
And to that I'd like to add that many people in need of mental health support are just too ill to search effectively for therapists, make a decision, follow it through. Your question "what are the barriers to seeking mental health support" just made me want to answer "my mental ill-health is the barrier".
I suspect that private therapy is actually more accessible to people who are quite high functioning, despite any difficulties they may have. There is nothing wrong with that, of course. Mentally well people seek therapy to improve their mental wellbeing just like physically healthy people go to the gym to improve their fitness. That is a good thing, something that everyone should feel is within their reach, ideally. But private therapy is often not a solution for people who have significant mental health problems.