Strauss was closely involved in two important events in 1936-37; the Unity campaign (of the Socialist League, the Independent Labour Party and the Communist Party), and the publication of the Socialist weekly Tribune. He was a leading signatory of the Unity Manifesto with Stafford Cripps, Aneurin Bevan and others. Although this campaign was a failure it remains a high-water mark in left-wing politics in the inter-war years. Subsequently, in 1938, Strauss campaigned for a Popular Front, to include the Liberals, progressive Conservatives and Independents. This activity resulted in his expulsion from the Labour Party, with Cripps and Bevan, in 1939.
Strauss was a member of the group which planned the launch of Tribune in January 1937. He served on the Board of Tribune for a number of years, wrote for the paper and continued to provide generous financial help at critical times later.
Elected to the London County Council at the early age of 22, Strauss served almost continuously as a Councillor from 1925 to 1946. He became a protege of Herbert Morrison, a powerful force in the London Labour Party, later leader of the LCC. They worked closely together to secure the first Labour majority on the LCC in November 1934, but they fell out over Strauss's left-wing activities. It says something of Strauss's character that he stood firmly by his convictions despite the fierce hostility of the Labour leadership of County Hall. However, he was able to make a substantial contribution to the work of the LCC as chairman of the important Highways Committee and with his colleagues he helped to provide a standard of local government which London had not seen before and has not seen since.
In his later years, Strauss moved from his previous position on the Left of the Labour Party, but he was never hostile to the radical views of a new generation of Labour MPs.