Principally from the right of British politics, anti-CND groups began to gather momentum in the early 1980s and peaked by the 1983 election. There are several valuable sources of information on this subject well worth reading.
Secret Society – Part 1: Secret Constitution – Secret Cabinet Committees
This fascinating programme looks at the British Constitution and how government does it’s work. The first part of the programme looks at the confidence vote of the Callaghan government and how it tried to influence the vote of the late Clement Freud. It also discusses with Peter, now Lord, Hennessey, the nature of secret cabinet committees.
The programme also takes an in-depth look at the pseudo-official opposition to CND and how various non-governmental pressure groups and thinktanks were mobilised to counter them. It looks at the “who” and the “whys” of the story and interviews Bruce Kent on his incredulity at the level of high placed opposition to CND. This would indicate to me the effectiveness of CND given how many senior figures were so concerned about its influence.