Routh was born at
Poole, Dorset, the 7th child, of The Honourable Richard Routh, Chief Justice of
Newfoundland, and his wife, Abigail Eppes. Three previous sons had died in infancy, so Randolph Isham was the fourth surviving child. His Father immigrated to
Salem, Massachusetts in 1764 at the age of 15 to take up the post of Assistant Customs Collector, and he married there Abigail Eppes of the Eppes family of
Virginia. During the
War of Independence, he took the Loyalist side and his refugee family itinerancy resulted in children being born in Salem,
Boston,
Long Island, New York, and
Halifax. A replacement position of Chief Customs Collector of Newfoundland was obtained eventually, and he went there to take up that post with his Brother-in-Law William Isham Eppes. His family, now located in England, remained in Poole, Dorset, where Randolph Isham was born in 1782. His Father operated for many years by commuting to Newfoundland annually for the warmer season to conduct customs business. Eventually, he was appointed Chief Justice of Newfoundland, but died on the passage to Newfoundland when his ship, the 16 gun sloop HMS Fly, disappeared and was lost at sea near
Cape Flattery in 1801. Randolph was educated at
Eaton College, but the death of his Father and the effect on the family finances after a few years forced them to curtail plans for a
Cambridge University education, and consider an army career. The Routh family had relatives in
Guernsey and Randolph's brother John Routh (b. Halifax 1777) was a business partner with the Guernsey Le Mesurier family in London.
Paul Le Mesurier was Lord Mayor of London 1893–94, and his brother Commissary General
Havilland Le Mesurier obtained an appointment for him in the Commissary Department of the British Army in 1805, as he had for his son Henry Le Mesurier. Henry Le Mesurier later became business partners in Montreal with John Routh's son, Haviland Le Mesurier Routh. Close ties between these families were maintained. ==Early army career==