Barna's birth name was Győző Braun, but because of anti-Semitism in Hungary at the time he changed his name to a Hungarian sounding name. In September 1939, during the outbreak of the Second World War, he and his wife were in America. Barna returned to Europe, in order to fight against the Nazis. He joined the British army as a parachutist, and fought in Yugoslavia. After the British withdrew from Yugoslavia, Barna remained in England. After the war he settled with his wife in London. He became a British national in 1952. Later he became a representative for the Dunlop Sports Company and continued traveling the world in this capacity. It was during one of these tours in 1972 that he succumbed to a heart attack in Lima, Peru.
In 1962 he published the book Table Tennis Today (London: Arthur Barker) and in 1971 Your Book of Table TennisISBN 978-0-571-09345-8. In 1957 he published the book "How to win at Table Tennis" (London: Pitman) ISBN 978-0-273-41699-9