He is best known for his appearances in Willy Wonka & the Chocolate Factory, Star Wars Episode IV: A New Hope, and the Harry Potter franchise.

[2] Goffe appeared as an Oompa-Loompa in the 1971 version of Willy Wonka & the Chocolate Factory and as a Jawa in Star Wars Episode IV: A New Hope, among a few other aliens.

He played Le Muff in the film History of the World Part I and also played Goober, a purple gremlin butler in the CBBC children's sketch show Stupid!

In 2007, Goffe played the lead role in A Kitten for Hitler, a film created by Ken Russell with the intention of making something as offensive as possible.

Goffe played a Jewish child who is made into a lamp by Hitler.