His father was the composer and conductor Francis Chagrin, who was born to Jewish parents in Bucharest, Romania, while his mother was Irish.

He attended St Marylebone Grammar School and subsequently the London Academy of Music and Dramatic Art.

[2] At the age of 17, Chagrin performed as a straight man to comedian Vic Oliver with whom he toured in England, Ireland and South Africa.

[4] After appearing in films such as Danger Route (1967), The Bliss of Mrs. Blossom (1968) and Alfred the Great (1969), he played Bill the Lizard in Alice's Adventures in Wonderland (1972), which notably featured Peter Sellers as the March Hare and Spike Milligan as the Gryphon, and he acted with Sellers and Milligan again in The Great McGonagall in 1974.

[6] From 1985 to 1987, he played the part of The Maestro in TV series The Orchestra which he also wrote and directed, alongside Sefi Rivlin.