His success in these popular satirical magazines raised his profile as a cartoonist and he soon began to have his work published in other publications such as the London Evening Standard, The Observer, The Sunday Telegraph, Radio Times and, later, The Oldie.
He collaborated with noted humorous writers and comic artists such as Ivor Cutler — providing the illustrations for his poetry books Gruts (1986), Fremsley and Life in a Scotch Sitting Room (1984) — and Monty Python members Terry Jones and Michael Palin — working on Bert Fegg's Nasty Book for Boys and Girls,[6] along with his wife Lolly and illustrators Frank Bellamy and Paul Buckle.
Honeysett's work was noted for its black humour, acerbic wit and sardonic, grotesque portrayal of characters who exemplified the cruelty, greed and stupidity of modern life.
His caricatures ranged from "moth-eaten grannies in wrinkled stockings, slippers and curlers, to slobbish youths with multiple piercings, baseball caps askew and falling-down jeans", all drawn in his distinctive "spidery" style of illustration.
At one notorious event during the party thrown for Private Eye’s 21st birthday, he reportedly threw a large cake over the head of the cartoonist Michael Ffolkes.