Hume was born in Westminster, London and baptized at St Mary's, Bryanston Square,Moulton (2004); Encyclopædia Britannica confused this with St.Mary Kent, while some older sources give his birthplace as Montrose, Forfarshire. The baptism register at St. Mary's, Bryanston Square records the date of registration as 15th July. a younger son (and the eighth child in a family of nine) of Joseph Hume, the Radical Scottish member of parliament, by his marriage to Maria Burnley. Until the age of eleven he was privately tutored growing up at the town house at 6 Bryanston Square in London and at their country estate, Burnley Hall in Norfolk. He was educated at University College Hospital, where he studied medicine and surgery and was then nominated to the Indian Civil Services which led him to study at the East India Company College, Haileybury. Early influences included his friend John Stuart Mill and Herbert Spencer. He briefly served as a junior midshipman aboard a navy vessel in the Mediterranean in 1842.
