Gravett's career began in 1981, as he and his "longtime partner" Peter Stanbury[2] managed the Fast Fiction table at bi-monthly Comic Marts held in Westminster Hall.

Gravett invited artists to send him their homemade comics, which he would sell from the Fast Fiction table with all proceeds going to the creator.

"[3] Later in 1981, Gravett was employed as promotions manager for Pssst!, an attempt to publish a British equivalent of the lavish French bande dessinée magazines.

Under the Escape Publishing imprint, they co-published Violent Cases by Neil Gaiman and Dave McKean, three volumes of Eddie Campbell's Alec between 1984 and 1986 and London's Dark in 1988 by James Robinson and Paul Johnson.

[9] Gravett and Stanbury's Great British Comics: Celebrating a Century of Ripping Yarns and Wizard Wheezes was nominated for a 2007 Eagle Award for Favourite Comics-related Book.