Self employment, no association member

Hello, everybody!

Is it right I can set up my own practice without being a member of any association? Instead, I am registering with HMRC and obtaining all the necessary licenses.
Does having an AATQB certificate restricts you off all of the above I mentioned?
I understand that you are not allowed to mention AAT if you do not keep their licence. Am I allowed to say that I am AAT qualified?

Thanks in advance.