I was on a PTSD board in a former life (LOL) and there were a lot of people from the UK on there. If you want trauma therapy through the NHS you do indeed have to work through their system in order to be referred for trauma therapy. Their resources are so thin that there is a waiting period and of course they want to reserve trauma therapy for those who actually need it, not those who walk off the street telling the docs that's what they want. (Not saying this is you, rather explaining the system.)

As for finding a private therapist, usually you can just find one and make the appointment, especially if you're "self pay".