Born in Staplehurst in Kent, Cramp worked as a gardener, before gaining employment with the Midland Railway. He worked as a porter based in Shipley and then Rotherham, where he was promoted to become a guard, and joined the Amalgamated Society of Railway Servants (ASRS). Soon after, he moved to Sheffield, where he married an Elizabeth Baker, also from Staplehurst.
Cramp was an effective trade unionist, and was elected to the executive of the ASRS in 1911, immediately prior to a major strike. The ASRS merged with other unions in 1913 to form the National Union of Railwaymen (NUR). Cramp maintained his position on its executive, working during World War I to oppose further strikes, and was elected as President of the NUR in 1917. He was also appointed as Industrial General Secretary of the union, a full-time position in which he was seen as deputy to General Secretary James Henry Thomas.
Cramp was also active in the Labour Party. He stood unsuccessfully for it in Middlesbrough West at the 1918 general election. He was a member of its National Executive Committee from 1919 until 1929, and served as Chair of the Labour Party in 1924/5. The following year, he was elected as President of the International Transport Workers' Federation. In 1929, he was elected to the General Council of the Trades Union Congress, serving for three years, thereby swapping positions with Thomas. In 1931, Thomas was given a ministerial position, and Cramp took over as General Secretary, but he died suddenly two years later.
- David Howell, "Cramp, Concemore Thomas Thwaites", Oxford Dictionary of National Biography
- Geert van Goethem, The Amsterdam International, p.129
- Hastings Lees-Smith, "Encyclopaedia of the Labour Movement", p.187
- "General Secretaries and Presidents of the ITF 1896-2010", International Transport Workers' Federation