Dunner succeeded Schonfeld in 1960 as head of the Union of Orthodox Hebrew Congregations, the umbrella organisation of chareidi Jewry in London, and as rabbi of Adath Yisroel. He retained both positions to the end of his life. He was also a critical figure in the Jewish Secondary Schools Movement, which had been started by Schonfeld during the Second World War to provide a more strictly Orthodox education than the diluted variant found in long-established foundations such as the Jews' Free School.