A parson's son from the Lincolnshire Wolds, Garvey was admitted on a choral scholarship to Trent College (Long Eaton) where he studied from 1916 to 1923. He then entered Emmanuel College at the University of Cambridge, where he read history and graduated B.A. in anthropology, while preparing to take the civil service examination, hoping to join the Indian Civil Service. He became involved in breaking the 1926 general strike, and did not find time to study for this examination, and instead applied for a position in the Colonial Service. He accepted a position in the Solomon Islands Protectorate, and sailed from Southampton to Fiji in November 1926.