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That list shows selection bias (Guardian etc) and different questions being used (e.g. In a February 2014 ComRes poll, 65% said they would feel uncomfortable living near a nuclear weapons base and 64% think there should be an international convention banning nuclear weapons.). Some of the questions are in the context of the economy, some are evoking nimbyism.
I wouldn't assume that what the CND present is really what the country thinks. They have an agenda, and however noble that agenda may be, are biased by it. This is shown by presenting a guardian poll as evidence that "a consistent majority of the British population are against nuclear weapons" without discussion of selection bias.
Polls are obviously just polls but it surely MPs' support for renewing/replacing Trident is highly undemocratic?
http://cnduk.org/campaigns/no-to-trident/opinion-polls