He was born at Buckhurst in Berkshire, the only surviving son of a minister, and graduated from Christ Church College, Oxford, in 1851, and 21 November of that year was called to the bar at the Inner Temple. He married Alice Eden, daughter of a bishop, in 1857, and finally entered Parliament as a Conservative, at the end of the year, having made several unsuccessful attempts previously.
He was a Secretary to the Treasury from 1866 to 1868, in the ministry of the 14th Earl of Derby, then was appointed to the Exchequer when Disraeli took office.
Hunt was appointed to the Admiralty for Disraeli's second ministry, serving from 1874 until his death from gout in 1877.
Although he was considered competent at finance, his turn at the Admiralty was not much admired. A very heavy-set person, he is said to have been responsible for the semicircle that is cut out from the end of the table in the Admiralty Board Room.
His residence was Wadenhoe House in Northamptonshire.