CNDは1957年に設立され、それ以降のイギリスの平和運動の最前線に存在し、ヨーロッパ最大級の単一争点の平和運動組織となった。1959年以降、復活祭の週末にかけて開催される、オルダーマストン近郊の原子兵器研究所(核兵器機関)からロンドンのトラファルガー広場までの「オルダーマストン行進」を組織している。なお最初の「オルダーマストン行進」は1958年に直接行動委員会(the Direct Action Committee)によって組織され、ロンドンからオルダーマストンへ行進した。
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