The concern here was nuclear power, not arms.

"Our external strategic objectives, as decided by delegates at our annual conference, are: ... 4) The closure of the Nuclear Power Industry."

Nuclear power is not, as a photograph of a banner on the CND's website tells me, the answer to climate chaos.

https://cnduk.org/about/aims-and-objectives/

Noted, but to the extent the Soviets may have aided the CND -- their interest seems to have been in its pro-disarmament, rather than its anti-nuclear industry stance.

If we go by the article you provided (and I am skimming it properly) - it doesn't mention nuclear power at all.

The nuclear disarmament movement achieved nothing and just because the Soviets supported something and maybe groomed some members doesn't mean they were pulling the strings. Having read about the KGB in London makes it seem like it was a pretty amateurish organization that never recovered from Operation FOOT. There are allegations that a leader of the Labour Party was a KGB agent, and still no one would insinuate that the Labour Party was a front of the KGB.