Gawler was the only child of Captain Samuel Gawler and his wife Julia, née Russell. Gawler's father was a captain in the 73rd Regiment of Foot, and he was killed in Mysore, India in December 1804. The Gawler family came from Devon. George Gawler was educated by a private teacher, then at a school in Cold Bath, Islington. He spent two years at the military college in Great Marlow.