In the 1950s and 1960s, Kibble became concerned about the nuclear arms race and from 1970 he took leading roles in several organisations promoting the social responsibility of the scientist. In the period 1970-1977 he was a national committee member, then treasurer, then chair of the British Society for Social Responsibility in Science; from 1976 he was a trustee of the Science and Society Trust; from 1981 to 1991 he was a national coordinating committee member, then vice-chair, then chair of Scientists against Nuclear Arms; he was a sponsor of Scientists for Global Responsibility; and from 1988 he was chair, and later a trustee, of the Martin Ryle Trust. He was chair of the organising committee of the Second International Scientists' Congress, held at Imperial College in 1988, and was a co-editor of the proceedings.