Damon joined the BBC in 1974 as a technical operator for radio news. His move into journalism took place in 1982 with a nightly phone in on LBC. Damon, with his wife Sian, spent seven years filming the downfall of the Soviet Union throughout Eastern Europe.  He then returned to the BBC to work as a presenter and reporter for BBC World Service and BBC Radio 4. During this time he was a regular presenter of PM.
In 2003 Damon became the main presenter of World Update on the BBC World Service. He presents the programme on weekdays at 1000 UK Time. During this time Damon has presented the programme on location around the world.