Littleblackdog, I think that if I were in your position I would follow the psychiatrist' recommendation and go for at least two or three sessions to what is on offer (the CBT). It's possible that either with a different therapist or because you'll be focussing on a different issue, your experience would be better than last time. If you find it damaging you could always cancel after two or three sessions rather than finishing the course? As you say since it's the NHS you unfortunately won't get much choice so I think I would take the attitude of trying out whatever is on offer.
Regarding what you said about CBT being too short and not going into the reasons behind the 'faulty thinking' - I think you are completely right about this. I see my T privately (he works for the NHS and also has a private practice). I did my own research before going to therapy, and so when I saw him for the first time, I went through the problems I was having and said that I thought I needed CBT. My T explained that because my problems were deeply rooted, CBT by itself probably wouldn't be effective, and schema therapy would be better. It's like CBT in some ways but it goes for longer and also you spend time on understanding why the 'lifetraps' or faulty ways of thinking have come about based on your life and working to change the emotions, not only the thoughts. Anyway it's just to say that my T explained that CBT by itself doesn't work for everyone, for these reasons, and it seems like this is what you have experienced. I also think there was a large study recently which showed that whether CBT is helpful depends a LOT on who is delivering it. You can be much more or less skilled at delivering CBT. So for that reason maybe it would be worth trying again?