 Morphett was born in London, the second son of Nathaniel Morphett, a solicitor, and his wife Mary, "née" Gliddon, of Cummins, Ide, Devon.When very young he was sent to a boarding school with Mme Pasquier in Wandsworth, and then to Webber's school in Teignmouth, Devon with his younger brother George.At 14 he went to the Manor House Academy, a school run by the mathematics writer Daniel Dowling at the top of Highgate Hill, London.