Honeyborne attended Ampleforth College and studied biology at the University of Newcastle-upon-Tyne. He joined the BBC Natural History Unit in 1992, working first for the commercial wing Wildvision and then on a number of live TV outside broadcasts from around the world.
He spent five years on attachment to John Downer Productions, co-directing the series Supernatural and Weird Nature, before returning to the BBC to make Wildlife on One documentaries with David Attenborough and to work on the strand Natural World (co-produced by Animal Planet and National Geographic Channel).
A keen scuba diver and photographer, he has also made a series of documentaries with world champion freediver, Tanya Streeter.
In 2009, he co-presented the BBC television series Wildest Dreams with Nick Knowles. In this reality TV series about wild animals, Honeyborne acted as mentor and judge to the candidates as they took on a series of filming challenges to compete for a placement at the BBC Natural History Unit.