Hume was born at St Mary Cray, Kent, the son of Joseph Hume, the Radical MP. He was educated at East India Company College, Haileybury, and then at University College Hospital, where he studied medicine and surgery. In 1849 he sailed to India and the following year joined the Bengal Civil Service at Etawah in the North-Western Provinces, in what is now Uttar Pradesh. His career in India included service as a district officer from 1849 to 1867, head of a central department from 1867 to 1870, secretary to the Government from 1870 to 1879 and in 1879 he went against the authorities and finally resigned in 1882.
It was only nine years after his entry to India that Hume faced the uprising of 1857 during which time he was involved in several military actions for which he was created a Companion of the Bath in 1860. Initially it appeared that he was safe in Etawah, which was not far from Meerut where the mutiny began. This however changed and Hume had to take refuge in Agra fort for six months. Only one Indian official remained loyal and Hume took back position in Etawah in January 1858. He built up a force of 650 Indian troops and took part in engagements with them. Hume blamed British ineptitude for the uprising and pursued a policy of ‘mercy and forbearance’.
In his early service as a District Officer in the Indian Civil Service, he began introducing free primary education and creating a local vernacular newspaper, Lokmitra = The People's Friend.