Jephson was the eldest son of Sir John Jephson of Froyle, Hampshire, an MP and member of the Irish Privy Council, and his first wife Elizabeth Norreys, daughter of Sir Thomas Norreys, Lord President of Munster, and Bridget Kingsmill.
Elizabeth brought to her husband the Norreys family's Irish estates at Mallow, County Cork and elsewhere.
Cromwell's refusal disappointed him bitterly: he suggested ironically that the word King should be removed from the English language, since it seemed to distress so many people.
[4] As a reward for his loyalty, in 1657 Oliver Cromwell sent him as envoy to Sweden while that country was at war with Denmark, and persuaded the two Kingdoms to enter a peace treaty.
In failing health, he retired to England, and spent his last months at Boarstall, his wife's family home in Buckinghamshire.