Among his notable works were the make-up effects for The Elephant Man, The Company of Wolves, and the stage musical The Phantom of the Opera.
[4] Tucker's earliest credited work is the make-up for the 1970 film Julius Caesar, starring Charlton Heston and John Gielgud.
[3] During 1975–76, he was part of the team that created the make-up and prosthetics for the iconic Mos Eisley Cantina scene in Star Wars.
[5] In 1980, Tucker was hired to create the prosthetics that would transform John Hurt into the hideously deformed Joseph Merrick in David Lynch's film The Elephant Man.
In the early 1980s, at the prompting of photographer Jay Myrdal, he fashioned a prosthetic that considerably enhanced the natural endowments of porn star Daniel Arthur Mead, who later gained notoriety under the pseudonym Long Dong Silver.
In 1985, he was nominated for BAFTA awards in the categories Best Make-Up Artist and Best Special Visual Effects for his work on The Company of Wolves.