Upon leaving Richmond Central State School, and after short spells in a sawmill and a boot factory, Tudor entered the felt hat industry, which he developed a passion for. Tudor apprenticed in Abbotsford and then travelled across Victoria in the hat trade. Tudor went to England, working in London, Birmingham, Liverpool and Manchester, marrying Alice Smale in Denton, Lancashire in 1894. Smale died the same year, however Tudor continued in the felt hat trade by moving to London and becoming vice-president of the local branch of the Felt Hatters' Union. In 1897 Tudor remarried to Fanny Jane Mead.
As vice-president of the union Tudor became interested in union politics (as many Labor politicians were before their entry into politics) and persuaded the British unions to adopt the union label principle. Returning to Australia, Tudor worked at Abbotsford's mills and took a seat in the Victorian Trades Hall Council. In 1900 he became president.
Tudor was immediately elected the Labor Party whip and assistant secretary. He ascended to the position of secretary in 1904, then Minister for Trade and Customs during the three Fisher ministries, from 1908-1909, 1910-1913, 1914-1915. When Billy Hughes replaced Andrew Fisher as the Prime Minister of Australia, Tudor continued in the role of Minister for Trade and Customs until 1916, when he resigned from the Hughes ministry over his opposition to conscription.
However, Hughes himself left the Labor Party at the end of 1916 to form the Nationalist Party.
In 1919 T. J. Ryan, then Premier of Queensland was transferred to federal politics to serve under Tudor as a deputy. Because of Tudor's incompetence, the party sought a new leader, and Ryan would have probably replaced Tudor if he had not died in 1921, leaving Tudor without a deputy.
Tudor was a quiet leader who did not intimidate the Hughes' government and was not considered a strong contender in the 1919 election. These predictions were correct and Labor was defeated again. In 1921 Tudor's health declined and was increasingly unable to fulfill his duties, however the party did not allow him to resign. Tudor died on 10 January 1922, becoming the first leader of the Labor Party to die 'in office'.