Born in Bristol, Barron attended Bristol Grammar School. Directly on leaving school, he started as a print journalist, working for the Western Daily Press in Bristol, before joining BBC News as a chief sub-editor in 1965.
Barron spent 40 years with the BBC, mostly overseas, starting as a producer with what became the BBC World Service. Barron was appointed Aden correspondent in 1967, covering the fall of that part of the British Empire, after which he became Cairo correspondent in 1968.
In 1971 he became South East Asia correspondent, and covered the Vietnam war, including in 1975 reporting against instructions from BBC Governors as the last US Army helicopter left Saigon, and as the North Vietnamese Army claimed victory. He then covered the Cambodian–Vietnamese War.
Based in Nairobi from 1977 onwards, covering all of Africa as chief correspondent, Barron covered the end of the regime of Idi Amin, and was the first foreign correspondent to reach an abandoned Kampala, filing a report from the headquarters of the State Research Bureau, Amin's secret police. Jon Snow, then a rival correspondent for ITN, commented that Barron was:
After Amin fled, Barron and cameraman Mohammed Amin, of Visnews in Nairobi, in 1980 located Amin to the Saudi Arabian city of Jeddah. Amin had been given refuge because of his conversion to Islam; after weeks of negotiation Barron secured the first interview with him since his deposition.
While still based in Africa, Barron later reported on the fall of Emperor Bokassa of the Central African Empire; and then the civil war in Rhodesia, resulting in the creation of Zimbabwe.
Returning to the United Kingdom in 1981, he became the BBC's all-Ireland correspondent, also spending three months covering the Falklands War from Chile, alongside longtime colleague Brian Hanrahan, who was with the British forces. Following a period in Washington D.C., he became chief Asia correspondent.
In 2000 Barron officially "retired", but still resident in Asia in 2003 he covered the First Gulf War, where he started reporting from the US Navy nuclear powered aircraft carrier, USS Theodore Roosevelt (CVN-71).
Relocated back to New York City from mid-2004, after official retirement from the BBC in late 2005, Barron and his cameraman Eric Thirer continued to work together. In 2007, 40 years after reporting on the end of that part of the British Empire, the pair returned to Aden.
Barron won the 1980 Royal Television Society award for Reporter of the Year, and then the International Reporting Prize for work in Latin America. He was also awarded the MBE for his services to broadcasting in 2006.
Barron and his wife Angela had a daughter, Fleur. He died, at the age of 69, of cancer at his family home in St Ives, Cornwall.