Lennox entered the House of Commons in 1846 as Member of Parliament for Chichester, in Sussex. He represented this constituency until 1885, when he stood for Partick, but was defeated.
Lennox held office in every Conservative government between 1852 and 1876. He was a Junior Lord of the Treasury in 1852 and between 1858 and 1859 in the first two short-lived governments of the Earl of Derby before becoming First Secretary of the Admiralty in 1866 in Derby's last government, a post he held until 1868, the last year under the premiership of his close friend Benjamin Disraeli. According to John F. Beeler in British naval policy in the Gladstone-Disraeli era, 1866-1880, Lennox acted as a spy to the then Chancellor of the Exchequer, Disraeli, informing him of the intentions of leading admirals.
He served again under Disraeli as First Commissioner of Works from 1874 to 1876 and was admitted to the Privy Council in 1874. He was forced to resign as First Commissioner of Works after revelations in the case of Twycross v Grant regarding the Lisbon Tramways swindle, of which company he was a director.
Hancock joined the Royal Navy in 1834. As a Commander he was regarded as an innovator in medical matters and insisted that the ship's surgeon had his own cabin. Promoted to Captain in 1855, he was given command of HMS Immortalité, HMS Trafalgar, HMS Duncan and HMS Duke of Wellington. He was appointed Commander-in-Chief, Pacific Station in 1876. He died in this role in September 1876.