Gunn was born in London, the son of George Gunn, a member of the London Stock Exchange, and Julia Alice Philp. His paternal grandparents were Theophilus Miller Gunn FRCS, a prominent London surgeon originally from Chard, and Mary Dally Battiscombe, from Bridport. Theophilus's father was John Gunn, a non-conformist preacher, brother of Daniel Gunn, originally from Wick in Scotland, but who spent most of his career in Chard. Both sides of the family were non-conformist. His unusual first name came from his grandmother's maiden name.