He was born at Haston Grove, Hadnall, Shropshire, son of Charles Alfred Bromley, a dyer, and his wife Martha Helen nee Wellings, and baptised at Hadnall on 6 August 1876. He was educated at elementary schools until the age of twelve, when he began working successively as a country post boy, a chemist's errand boy, and assistant on W.H. Smith & Sons' bookstall at Shrewsbury railway station. At age fourteen he began working for the Great Western Railway as an engine cleaner at Shrewsbury. In 1892 he became an assistant fireman, and a regular fireman in 1896. He was a registered train driver in the GWR until 1905.
Becoming a fireman qualified him to join his trade union, the Associated Society of Locomotive Engineers and Firemen.He became active in union branches in Shrewsbury and, as he moved employment in the GWR, at Worcester and Southall, Middlesex. In 1903 he joined the GWR locomotivemen's negotiating committee and in 1908 became ASLEF representative on the sectional conciliation board. In 1909 he became its organiser in the North of England, based in Manchester. In succession to Albert E. Fox, he was elected with clear majority to national general secretary in October 1914. When the railway companies were brought under government control during the First World War, he was a railway unions representative on the Advisory Committee to the Ministry of Transport. During the same period, as his union's head he campaigned for the interests of its trades against the claims of rival railway unions and secured an agreement in December 1918 for a standard eight-hour day for locomotive footplatemen. In 1919 he obtained a full standardisation of locomotivemen's wages and service conditions. By that year the union's membership had grown from 32,200 in 1913 to 57,184. In January 1924 he led a nine-day national locomotivemen's strike against worsening working conditions. He was a founder member of the General Council of the Trades Union Congress in 1921. He attended the TUC's first delegation to visit the Soviet Union in 1924. He served as President from 1932 to 1933 and retired as ASLEF general secretary in 1936.
Bromley married in Shrewsbury, on 6 March 1901, Ann Hall. After his retirement from union leadership in 1936 they moved to Cornwall where he died of a cerebral haemorrhage at his home, Mon Repos, Borras Cross, Liskeard, aged sixty-nine. He was cremated at Efford Crematorium, Plymouth, Devon.
