In 1969, after his graduation from university, Browne joined the Foreign and Commonwealth Office. His first posting to Iran was as Third Secretary in Tehran from 1971 to 1974. From 1976 to 1980, he was on loan to the Cabinet Office. Following the Iranian Revolution in 1979, he was asked by then foreign secretary David Owen to head an inquiry into why the Foreign and Commonwealth Office had failed to predict the fall of the Shah. In early 1980, he was posted to Southern Rhodesia as First Secretary and Head of Chancery. He attended the festivities that saw the transition of the country from Southern Rhodesia to Zimbabwe on 17/18 April 1980. Between 1981 and 1984, he was Desk Officer at the Maritime, Aviation and Environment Department of the Foreign and Commonwealth Office. From 1984 to 1989, he served as First Secretary at the British embassy to the European Economic Community. His specialism was the environment. In 1989, he was appointed chargé d'affaires to Iran in Tehran. However, three weeks after he took up the post diplomatic relations were broken off between Britain and Iran due the Rushdie Affair. He served in London as a Foreign and Commonwealth Office counsellor. From 1990 to 1994, he was posted to the United States; first to Washington, D.C. as press and public affairs counselor and then to New York City as British information head. Between 1994 and 1997, he was Head of Middle Eastern Department, Foreign and Commonwealth Office, in London. In 1997, he was posted to Iran as chargé d'affaires. In the 1999 Queen's Birthday Honours, he was appointed Companion of the Order of St Michael and St George in recognition of his work in Iran. He was promoted to ambassador in 1999 and oversaw the visit to Tehran in late September 2001 by then foreign ministerJack Straw, the first visit to the country by a senior a British government minister since the 1979 Revolution. He left Iran in 2002 and was appointed Knight Commander of the Order of the British Empire in that year's Queen's Birthday Honours in recognition of his work as ambassador. He served as Ambassador to Denmark from 2003 to 2006.
Browne married Diana Aldwinckle in 1969. They had met while fellow undergraduates at the University of Oxford. Together they had two sons, Jeremy and Arthur, and two daughters, Jasmine and Abigail. He was an avid rock fan with a large collection of vinyls. In 1980, he had attended one of the last concerts by Bob Marley at the Rufaro Stadium, Salisbury, Zimbabwe.