Heraldic Art - Codrington Arms, 1877

He entered the Royal Navy in 1823 in took park in operations against pirates, while supporting the blockade of Algiers. He served in the squadron off Greece, during the Greek War of Independence. In October 1827 he was present at the Battle of Navarino where the allied fleet was commanded by his kinsman Vice-Admiral Sir Edward Codrington. During the battle Henry acted as signal midshipman and was wounded and, following the action during which the Ottoman fleet was destroyed, he was awarded the Russian Order of St. Vladimir, the French Legion of Honour and the Greek Order of the Redeemer for his services. Promoted to captain in 1836, he appointed to HMS Talbot and undertook a survey of enemy positions prior to the bombardment of Acre in November 1840 during the Egyptian–Ottoman War. For this service he was appointed a Companion of the Order of the Bath.

Codrington went on to command HMS Queen, as Commander-in-Chief, Portsmouth, in March 1841 and then to command the first-rate HMS St Vincent, his father's next flagship as Commander-in-Chief, Portsmouth, in October 1841. He became commanding officer of the HMS Thetis in the Mediterranean Fleet in October 1846 and provided refuge on board ship for Leopold II, Grand Duke of Tuscany and his family who were fleeing from revolutionary forces in 1848.Codrington commanded the Royal George in the Baltic in October 1853 and took part in naval operations during the Crimean War. Admiral Sir Charles Napier threatened to court-martial him for failing to achieve the required standards but the Admiralty refused to support this course of action. Promoted to Commodore, he was given command of a squadron of gunboats in February 1856. The Admiralty envisaged that he would lead a mission to attack the naval base at Kronstadt but the War ended with the Treaty of Paris in March 1856 and the mission was abandoned.