I do think the police should act to try and prevent violent groups from committing violence. Your position seems to be that the state should accept violence as long as the people committing it claim to be political? If anything organised political violence is the type of violence that it's the most important to prevent because it has by far the largest potential for harm.
I can talk about specific things the UK police have done when targeting 'extremist' groups and how I disprove of them if you want (undercover police assuming fake identities to the extent of having children with women in the targeted groups being one). But disapproving of specific things isn't the same as saying the police shouldn't be investigating and infiltrating organisations advocating violent ideologies.