He was deeply involved in the crisis of the British Communist Party in 1956, following the Soviet invasion of Hungary. Khrushchev's denunciation of Stalin in 1956, or, more exactly, the failure of the British CP leadership to recognise its significance, transformed the Historians' Group from loyalists into vocal critics. Saville's was the first voice raised at its meetings. Breaking his affiliation with the cluster of British Marxist historians known as the Communist Party Historians Group, Saville emerged as one of the founders of the "New Reasoner", in partnership with another Yorkshire Communist historian, E.P. Thompson, part of a group of dissident Marxists who condemned the Soviet intervention in Hungary in 1956.