Muirhead-Gould was born in London. He was the son of Arthur Lewis Gould and Emily Gertrude Lilias Muirhead. He joined the Royal Naval Cadets in January 1904. During World War I, he earned a Distinguished Service Cross, and was recognised as a Chevalier (Knight) of the Légion d'honneur and a Chevalier of the Order of the Redeemer. Between 1933 and 1936 Muirhead-Gould was a member of the Naval Intelligence Division, assigned to the British Embassy in Berlin. During this time he kept Winston Churchill informed of the German military buildup, particularly in relation to the Treaty of Versailles and the later Anglo-German Naval Agreement.