The Prime Minister said Admiral Woodward, the commander of the Royal Navy Task Force that retook the Falklands Islands in 1982, was a “truly courageous and decisive leader” ane that Britain was “indebted” to him.
Admiral Woodward reportedly died after a long illness.
Mr Cameron said: “I am saddened to hear that Admiral Sir John ‘Sandy’ Woodward has passed away. The admiral was a truly courageous and decisive leader, proven by his heroic command of the Royal Navy Task Force during the Falklands conflict.
“We are indebted to him for his many years of service and the vital role he played to ensure that the people of the Falkland Islands can still today live in peace and freedom.”
Defence Secretary Philip Hammond commended Admiral Woodward on his “magnificent achievement” and said he would be remembered by many as the Navy’s “fighting admiral”.
Mr Hammond said: “Admiral Woodward served his country with distinction throughout his career, but he will be best remembered by many as the Navy’s Fighting Admiral after he led the Royal Navy Task Force, sent by Margaret Thatcher, to re-take the Falkland Islands in 1982.
“Following this magnificent achievement he served as the Deputy Chief of the Defence Staff and went on before retirement to be the Flag Aide-de Camp to the Queen.”
First Sea Lord Admiral Sir George Zambellas said Admiral Woodward was highly regarded and widely respected in the military.
He said: “Undaunted by the challenge of fighting a capable enemy over 8,000 miles from the UK, in the most demanding and extreme of weather conditions, and against uncertain odds, Admiral Woodward’s inspirational leadership and tactical acumen was a major factor in shaping the success of the British forces in the South Atlantic.”
Admiral Woodward was born in Penzance, Cornwall, on May 1 1932, according to the Who’s Who annual.