I had a brilliant CBT therapist and went for over a year. But this was 2006.
The standard offer locally now is actually 10 sessions, 6 is not enough, 10 imo doubtful, but thats what's on offer with resources strapped MH services: its sometimes extended.
It is very good for tackling issues where understanding your patterns of thinking without digging deeply is helpful, and it does help quite a few people. But imo 10 sessions is not enough. Also level of training of therapist and whether there is a therapist person match.
so CBT is structured problem solving therapy working with "in the present issues" but longer term CBT with a good therapist can offer more than described above
Counselling is person centred , usually lasts longer, but is mainly still designed to work on problems inhale here and now, not opening deep pandoras box of the past. There are many different sorts and what matters is that you feel the counsellor is "right for you"
Psychotherapy lasts substantially longer and does go back to when problems and issues begun -childhood or a traumatic point. To do it you have to be able to cope with triggers that this "digging up" throws up. You develop a relationship with the therpaistand your reactions to them start coming out - ie feelings of anger or love or resentment towards the therapist, and that all part of the package.
Psychoanalytic psychotherapy is where you lie down and dont see the face of the therapist. Often more than once a week. Definitely deep and can be disturbing and is not often recommended if serious MH problems unless there is other MH support as in a CPN (Community Psychiatric Nurse).
I know this because I am a trained psychotherapist but have also experienced CBT, counselling, and psychoanalytic psychotherapy as a patient more recently (until 2014 - still NHS funded then)..
They have all had their place and I was fortunate enough to get them when the NHS still offered them. Some limited counselling and therapy is still available on the NHS but TBH hard to get.
At lot of people now decide its so important they will try and allocate more for it - £40 0r upwards substantially, although there are some voluntary sector funded opportunities, and some opportunities to get grants for counselling. for example locally there is a free counselling charity for abuse victims, but a long wait.
If you decide to go private you need to check out that they belong to appropriate professional bodies and have had the training. There are actually quite a number of ex NHS counsellors who are very good: some have sliding scales.