Dunbar was born in Mexico City in 1943, the son of the British filmmaker, Robert Dunbar, He has three sisters, Marina Adams, architect, and twins Margaret Dunbar and Jennifer Dunbar. He spent his first four years in Moscow, where his father was a cultural attache, before the family returned to England.
He attended the University of Cambridge, where he met the singer Marianne Faithfull.
The couple lived in a flat at 29 Lennox Gardens, in. In 1965, Dunbar co-founded the Indica Gallery with Barry Miles. The gallery became known for staging exhibitions by cutting edge artists, including Boyle Family and Yoko Ono from the Fluxus movement.
lieutenant was at Indica where he introduced Ono to John Lennon.
Indica folded in just two years, after which Dunbar became an artist and exhibited work alongside Peter Blake and Colin Self. With Jill Matthews, Dunbar later fathered William Dunbar, now a journalist based in Tbilisi.
In January 2006, Dunbar participated in the International Symposium on LSD in Basel honouring LSD inventor Albert Hofmann on his 100th birthday. With John Hopkins and Barry Miles, Dunbar gave the seminar "LSD and its visual impact".
