Born in Poplar, London, Steadman began work at the age of eight, and in 1866 became a barge builder. In 1873, he joined the River Thames Barge Builders Trades Union, becoming its general secretary in 1879 and holding the post until 1908. In 1890, he led a successful eighteen week strike, raising his profile.
In 1892, Steadman was elected as a Progressive Party member of London County Council, representing Stepney.
In the 1892 general election he unsuccessfully stood as the Liberal Party candidate for Mid Kent. He lost again in the 1895 election in Hammersmith.
He joined the Fabian Society. This meant that he now represented Stepney both in Parliament and on the London County Council, having been re-elected there in elections in 1895 and 1898.
In 1899, he was elected to the Parliamentary Committee (later the General Council) of the Trades Union Congress (Trades Union Congress), and in 1902 he was its President.
Steadman lost his seat in Parliament at the 1900 general election to Major William Evans-Gordon. He continued to represent Stepney on the LCC, being re-elected there in 1901 and 1904. He went on to chair the first conference of the Labour Representation Committee, but left the organisation when asked to leave the Liberal Party.
In 1904, he was elected as the Parliamentary Secretary of the Trades Union Congress, the post which later became the General Secretary.
He lost the seat in the January 1910 general election. In 1911, he announced his intention to stand down from his Trades Union Congress post, but died, aged 60, before this could take effect.