In the mid-1970s Barrett was cast in the BBC Radio series of George Simenon's Inspector Maigret novels as Maigret's subordinate, Inspector Janvier. He has performed the voices of Asterix, Caius Tiddlius, Fulliautomatix, Roman Ghost, Cylindric, Mannikinpix, Gladiator Trainer and Jailer in the English version of The Twelve Tasks of Asterix, Tik-Tok in Return to Oz, a Goblin in Labyrinth, Big Mac and other characters in TUGS, Thadius Vent's soothsayer Goodtooth in Oscar's Orchestra, Melchoir in the English dubbed version of the Lapitch the Little Shoemaker TV series, Roly the Pineapple in the English version of The Fruities and UrSu the Dying Master and UrZah the Ritual-Guardian in The Dark Crystal as well as additional characters in two video games The Feeble Files and Viking: Battle for Asgard. He also provided the voice for Captain Orion in Star Fleet, the English version of the 1980s Japanese puppet series X-Bomber.
In 1996, he was the narrator for the Channel 4 documentary series, Black Box. The series primarily concentrated on commercial aviation accidents, and the investigations related to them.
Barrett also worked as part of an ADR Loop Group on Aardman's animated film Flushed Away, a voice director on Lapitch the Little Shoemaker and a dialogue director on The Fruities. He has also narrated episodes of the BBC TV series People's Century and Dancing in the Street, as well as a number of BBC nature documentaries in the late 1990s and early 2000s.