Anthony was the fourth and youngest son of the 2nd Baron St. Oswald and his wife Mabel Susan Forbes. Both his parents died in 1919. He had an older sister.
The Winn family had owned the Nostell Priory estate near Wakefield since the 1650s. It was given to the National Trust in 1953.
He was educated at Eton and Matriculated in 1928, coming up in the Hilary Term. He appears not to have gained a degree.
On 2 January 1931, he sailed to Lisbon with his friend Harry Oppenheimer. They returned to England on the 16th. His address on the manifest is both 10 Charles Street and Christ Church. Both of them were students. [Harry Oppenheimer, a son of Sir Edward Oppenheimer, came up in the Michaelmas Term 1927 and read PPE. He was made an Honorary Student of Christ Church in 1974 and died in 2000].
On Christmas Eve 1932, Anthony left Southampton for South Africa describing himself as a journalist. He appears not to have returned until 18 February 1936 when he arrived from Sydney. His address was c/o White’s Club, St. James’s.
Anthony was Lobby Correspondent for The Times in 1938 at the time of the Munich Agreement. When the editor, Geoffrey Dawson, altered his report on Duff Cooper's resignation and published it as "From our Lobby Correspondent", Anthony resigned.
He joined the 16th London Regiment (Queen's Westminster and Civil Service Rifles) a Territorial Regiment. In 1937 it was transferred to the King’s Royal Rifle Corps being renamed as the Queen’s Westminsters. At the outbreak of war, it became the 1st Battalion and the 11th KRRC in 1941.
As part of the 24th Armoured Brigade they arrived in North Africa in late July 1942. They took part in the Second Battle of El Alamein from 23 October–11 November.
He was killed on 26 October and is buried in the El Alamein War Cemetery, Plot X. E. 9.