- Alexander was a senior Royal Navy commander during the Napoleonic Wars. Born a son of the Scottish peer Thomas Cochrane, the eighth Earl of Dundonald, Cochrane joined the Royal Navy as a boy and served with British naval forces in North America, where he saw service in the American War of Independence.
Cochrane also participated in the Egyptian operations in 1801. When Alexandria fell, Cochrane, in the 74-gun third rate HMS Ajax, with the sixth rate HMS Bonne Citoyenne, the HMS Cynthia, the brig-sloops HMS Port Mahon and HMS Victorieuse, and three Turkish corvettes, were the first vessels to enter the harbor.
In 1805 he was made commander of the Leeward Islands station. He conducted operations against the French and Spanish at the Battle of San Domingo on 6 February 1806 in which a cannon ball blew his hat off his head while he was on the deck of his flagship, HMS Northumberland. He was appointed GCB (Knight Grand Cross of the Order of the Bath) on 29 March 1806.
Other rewards included thanks from both Houses of Parliament, freedom of the city of London, and a sword valued at 100 guineas. In 1807 he sailed in HMS Belleisle (74 guns) in the expedition against Danish Islands, and in 1809 commanded naval forces in the Conquest of Martinique.
From 1814, during the War of 1812, Cochrane, then a vice admiral, served as Commander-in-Chief of the North American Station, based at the new dockyard in Bermuda. He landed the force under General Ross that burned Washington and also pushed successful naval foray's at the same time. Initially he wanted to attack Rhode Island after the success at Washington, but was dissuaded by Ross and Admiral Cockburn who wanted to go after the bigger prize of Baltimore. During the Battle of Baltimore, he was responsible for the bombardment of Fort McHenry in Baltimore, Maryland which proved ineffectual and he resisted calls to more aggressively attack the fort by frigates. He did order a diversionary raid by boats to assist the Army encamped near Baltimore in their proposed attack on Hampstead hill (which they canceled and withdrew), but this diversion also had no success. The Army and Navy's failure at Baltimore effectively canceled out the success of Washington. The use of bomb vessels and rocket ship was the event which gave rise to Francis Scott Key's poem which became "The Star-Spangled Banner". He also led the British force that won the Battle of Lake Borgne in December 1814 and succeeded in giving the Army a hard short road to New Orleans for which to advance. However, the Army was defeated at the Battle of New Orleans in January 1815. The Battle of New Orleans was actually fought after Britain had signed a Treaty of Peace that was in transit to Washington for ratification.
The Duke of Wellington held that the failure of the New Orleans campaign was largely the fault of Cochrane, commenting in eulogy to General Edward Pakenham, killed at New Orleans, that:
"I cannot but regret that he was ever employed on such a service or with such a colleague. The expedition to New Orleans originated with that colleague... The Americans were prepared with an army in a fortified position which still would have been carried, if the duties of others, that is of the Admiral (Sir Alexander Cochrane), had been as well performed as that of he whom we now lament."
Despite the lack of success and damage to British prestige that occurred by the defeat of British forces at the Battle of New Orleans, Cochrane was promoted to admiral in 1819. From 1821 to 1824, he was Commander-in-Chief, Plymouth.
His death, which occurred at Paris, was fearfully sudden. Accompanied by his brother he went, on the morning of the 26th of January, 1832, to visit his daughter, Lady Trowbridge, for the purpose of inviting his young grand-children to an evening entertainment; but while he was affectionately caressing them he suddenly started, placed his hand on his left side, and exclaiming to Mr. Cochrane, "O brother, what a dreadful pain!" he fell back into his arms, and instantly expired.