I went to NHS speech therapy at around 21 about ten years ago. I don't remember a very long waiting list. I think I had around 10-12 sessions and it was enormously helpful. I also deal with a lot of shame about my stuttering. I have horrible memories of speech therapy as a child and I told the speech therapist this and she was very understanding. I told her that old school fluency techniques were like torture to me and we did sessions very much based managing my attitude around stuttering, understanding my stutter better, reducing avoidance etc. I obviously still stutter and I think I'll always have some shame about it, but I found that reducing that shame and avoidance actually reduced my stutter and of course made my life a lot less stressful.