 Born the son of Francis Cargill Begg and Muriel Clare Begg (née Robinson), Begg was educated at St Andrew's School, Eastbourne and Malvern College, before joining the navy as a special entry cadet in September 1926.Promoted to midshipman on 1 September 1927, he was posted to the cruiser on the China Station in October 1927 and then to the battleship in the Atlantic Fleet in April 1929.Promoted to sub-lieutenant on 1 November 1929 and to lieutenant on 1 December 1930, he joined the cruiser in the Mediterranean Fleet in April 1931 before training as a gunnery specialist at the shore establishment in 1934.