Jeremy Varcoe was born 20 September 1937, son of Ronald A. G. Varcoe and Zoe E. Varcoe (née Lovering). He was educated at Charterhouse and Lincoln College, University of Oxford (MA). In 1961 he married (1st), Wendy Anne Moss (died 1991), having two daughters; and in 1995, he married (2nd), Ruth Murdoch (née Wallis). After his National Service, with the Royal Tank Regiment, 1956–58, Varcoe joined the Colonial Service, as a District Officer in Swaziland [later Eswatini], 1962–65. He then briefly joined the legal profession, being called to the Bar at Gray’s Inn in 1966 and working as a Lecturer in Law at the University of Birmingham, 1967–70.

Varcoe then joined the Diplomatic Service, and his service included: Rhodesia [later Zimbabwe] (Political) Department, Foreign and Commonwealth Office, 1970–72; Deputy Secretary General, Pearce Commission on Rhodesian Opinion, 1972; First Secretary, Ankara [Turkey], 1972–74, Lusaka [Zambia], 1974–78; Central and Southern African Department, FCO, 1978–79; Counsellor, Kuala Lumpur [Malaysia], 1979–82; Head of Southern African Department, FCO, 1982–84; Counsellor, Ankara, 1984–85; on special leave with Standard Chartered Bank, Istanbul, 1985–87; Ambassador to Somalia, 1987–89; Minister/Deputy High Commissioner, Lagos [Nigeria], 1989–90; Assistant Under-Secretary of State, FCO, 1990–92.