He entered the Indian Civil Service in Bombay in 1860, served as District Judge and Judicial Commissioner in Sind; acted as secretary to Bombay Government, Judicial and Political Departments; and from 1885 acted as Judge of the High Court, Bombay. He retired when acting Chief Secretary to the Government of Bombay in 1887. During his work he noted the troubles of peasantry arising from moneylending and he suggested that co-operative agricultural banks be established to provide credits at reasonable rates. The proposal was supported in India but was blocked by the India Office. Wedderburn supported reforms suggested by Lord Ripon to develop local self-government and equality to Indian judges. He was seen as supporting the aspirations of Indians and was denied a judge position in the Bombay high court. This led him to retire early in 1887. Along with Allan Octavian Hume he was a founder of the Indian National Congress and served as its president in 1889 and 1910. He worked along with influential Congress leaders in Bombay and in 1890 he chaired the British committee of the Indian National Congress, helped publish the journal India and attempted to support the movement through parliamentary action in Britain. He developed a close working relationship with G. K. Gokhale of the Congress. He was an unsuccessful parliamentary candidate in North Ayrshire in 1892 and served as LiberalMember of Parliament for Banffshire from 1893 to 1900. He was a member of the Royal Commission on Indian Expenditure in 1895 and chairman of Indian Parliamentary Committee. He was considered a great friend of the Indian Progressive Movement and presided at the Indian National Congress, 1889, later Chairman, British Committee of the Indian National Congress. In 1910 he returned to India as Congress president and tried to solve the rift between Hindus and Muslims and attempted to reconcile the differences between those who wished to work constitutionally and those who wanted to use more militant actions. He wrote a biographical memoir of A. O. Hume who died in 1912. He succeeded his brother, Sir David, to the baronetcy on 18 September 1882. He married Mary Blanche Hoskyns, daughter of Henry William Hoskyns, on 12 September 1878. A daughter, Dorothy, was born in Poona in 1879 and in 1884 they had a second daughter in London, Margaret Griselda. He died at his home in Meredith, Gloucestershire on 25 January 1918.
Publications
Papers and Schemes on Arbitration Courts, Agricultural Banks, Village Panchayets and subjects relating to the condition of the Indian people
