The son of John Davys of Rempstone, Nottinghamshire, by Sophia, daughter of the Rev. B. Wigley of Sawley, Derbyshire, was born at Loughborough, Leicestershire, 1 October 1780.
In 1757 Calcraft purchased an estate at Rempstone on the Isle of Purbeck in Dorset, which gave him an interest in three nearby parliamentary boroughs, Corfe Castle, Poole and Wareham.
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John Calcraft the elder (1726 – 23 August 1772), of Rempstone in Dorset and Ingress in Kent, was an English army agent and politician.