A talented chess player, he won the first British Boys' Championship in 1923. He made his international debut at the strong London tournament in 1932 tournament. His best results in international competition were achieved in three straight years at the Margate tournaments from 1937–39, and at Hastings 1938. In all four events he finished just above the middle against strong fields, with performance ratings (as calculated by Chessmetrics) between 2538 and 2565. This places him at a solid International Master standard although he never received this title.
He represented England in the Olympiads of 1937, 1939, 1952 and 1956. The 1956 Olympiad trip to Moscow was risky since Britain and the USSR were by then locked into the Cold War and Milner-Barry's wartime codebreaking knowledge would have been of great interest to the Soviets; the fact that Britain had broken German codes on a massive scale was kept secret until 1974 when The Ultra Secret was published.
Milner-Barry finished second in the British Chess Championship at Hastings 1953 which was his best result in British Championships. He was president of the British Chess Federation between 1970 and 1973, competed in the British Championship as late as 1978 and was still competing local events into his 80s. George Koltanowski wrote that, "his style was very pleasing to spectators because he was always looking for dangerous continuations and quite often he found them!"
Michael Haygarth was a regular competitor in the British Championships during the early 1960's. He was a regular in the British Championship from 1959 to 1979, winning it in 1964. Not much is available on Haygarth, but he appears to have retired from chess in the late 1960s, but returned for another ten years after Fischer won the world championship. In the 1974 British it was his defeat of Jonathan Mestel that caused a seven-way tie which was eventually resolved in favor of George Botterill. Haygarth passed away peacefully in the hospital on April 27, 2016 at the age of 81.