I am not familiar with the legislation of the United Kingdom, but judging by the common legal framework, the state does have levers to restrict the activities of a particular organization for various reasons. I emphasize restriction, not prohibition. Prohibition requires a completely different reality. First, it is necessary to clarify what you mean by an organization, its legal form, and then what the state is being accused of, what actions… By way of example, I can say that in Georgia the state can do virtually anything (unfortunately).
Yes, but only in extreme cases—like if the group is linked to crime or real threats to security. The key is due process and solid evidence. If the ban is just to suppress voices, that’s when it violates civil liberties.