Henry Ralph Crooke was born in Calcutta [India] on 7 December 1875, the eldest son of Frederick James Crooke and Louisa Maud Rich. He was educated at Fosters, Stubbington House [Hampshire], and then aboard HMS Britannia. In 1916 he married Lilian Ethel, widow of the late Colonel E. P. Smith, and daughter of the late Colonel C. E. Harman; they had no children.

Crooke enlisted on Britannia in 1888, at the age of 12, becoming a Midshipman in 1890, and subsequently serving as Midshipman on HMS Camperdown, HMS Raleigh, and HMS Active. While on HMS Active, Crooke was promoted to Acting Sub-Lieutenant in 1894, becoming a full Lieutenant in the following year. He then moved to HMS Calypso as Watchkeeper Lieutenant between 1896 and 1897, before specialising in gunnery (1897-1899) and serving as a Junior Staff-Officer in HMS Excellent (1899-1900). Crooke served as Gunnery Lieutenant in HMS Repulse, (1900-1903), then as an instructor and Experimental Officer back in HMS Excellent, until 1905. At the end of that year, Crooke was promoted to Commander, and came ashore to work as Assistant to the Director of Naval Ordnance [John Jellicoe], until 1907. He then returned to sea, first as Commander of the cruiser HMS Good Hope, (1907-1909), and then of another cruiser, HMS Black Prince (1910-1912), at the end of which time he was made Captain. During the last three months of 1912, Crooke took part in the Boom Defence Committee and Director Committee before returning to the Admiralty as Assistant Director of Naval Equipment from February 1913 until the outbreak of war in August 1914. He commissioned the light cruiser HMS Undaunted, in August 1914, and then fitted out a similar ship, HMS Caroline, serving in her in the 1st and 4th Light Cruiser Squadrons until April 1917, and being present at the Battle of Jutland (for which he was mentioned in despatches, and was awarded the Order of St Anne of 2nd class, crossed swords). On leaving the Caroline, Crooke then became Captain of HMS Excellent (Gunnery School), between April 1917 and June 1918, and then Director of Naval Ordnance, at the Admiralty, (1918-1920). Returning to sea once more in March 1921, he took command of a series of battleships, starting with HMS Benbow, in March 1921, then HMS Emperor of India, in April 1921, HMS Ajax, from October 1921 until early 1922, and finally HMS Marlborough, from March-September 1922. At the end of this time he was promoted to Rear-Admiral, and had to return to shore once again, initially as an aide to King George V (1922), then as Vice-President of the Ordnance Committee at the Royal Arsenal, between 1924 and 1927 (and as President from 1927 to 1928). In January 1928 he was promoted to Vice-Admiral and retired, being promoted to full Admiral in 1932. The Second World War saw Crooke return to active duty, serving as Commodore, Royal Naval Reserve, on convoy duties, from September 1939 to January 1942, then as a Captain in the Royal Navy from June 1942 until the end of 1944.

Crooke was awarded the CB in 1919, and the KBE in 1940. He died on 11 February 1952.