Born in St. James's Street, Piccadilly, on 5 October 1751, he was the elder son of Thomas Shore of Melton Place, near Romford, an East India Company employee, by his wife Dorothy, daughter of Captain Shepherd of the Company's naval service. At the age of fourteen Shore was sent to Harrow School. In his seventeenth year Shore was moved to a commercial school at Hoxton for the purpose of learning bookkeeping, to take up an opportunity made for him by the merchant Frederick Pigou, a family friend. Towards the close of 1768 he sailed for India as a writer in the East India Company's service.