Between shameless scientific fraud from last century still affecting and harming nuclear policy to this day [0], and masses of idiots being easily influenced and swindled by foreign powers [1] (example specifically about the UK's case), I don't know why any such parties haven't been forcefully disbanded or put in the same category as terrorists, along with other organizations such as "Green"-"peace". They have at large done immeasurable damage to their countries and the world at large, and most of them started out explicitly as being anti-nuclear, that being their only mission for the longest time, only becoming relevant through the most disgusting fearmongering. Most importantly, they've achieved nothing but ensure the continued, worldwide permanent reliance on oil states and the terrorism that derived from it.
0. https://atomicinsights.com/wp-content/uploads/LNT-and-NAS-En...
1. https://en.wikipedia.org/wiki/Campaign_for_Nuclear_Disarmame...