Perkins read English at Lincoln College, Oxford and while there wrote for and directed The Oxford Revues of 1974 and 1975, contributing to, among others, a comedy production called Radio Active. After his time at Oxford, Perkins joined the Ocean Transport and Trading Company "(in the same intake as his confrère Portillo), [where] Perkins was put to work studying waste timber in Liverpool." Perkins did not last long in the field of commercial shipping, however (nor did Portillo). In 1977, drawing on his work for the Oxford Revue, Perkins joined "BBC Radio's light entertainment department [alongside] Cambridge graduates such as John Lloyd and Griff Rhys-Jones.
In mid-1977, Perkins produced the first series of Douglas Adams' The Hitchhiker's Guide to the Galaxy for BBC Radio 4, taking over from pilot-producer Simon Brett. Perkins aided and assisted the notoriously slow writer in finishing the scripts, before John Lloyd "was drafted in to write large sections of the later episodes." Perkins also drew "on the resources of the Radiophonic Workshop" to help create the groundbreaking audio effects for the series.
"The intellectuals compared it to Swift," noted Perkins, "and the 14-year-olds enjoyed hearing depressed robots clanking around."
In 1986, Perkins married Lisa Braun, "a BBC studio manager on The Hitch-Hiker's Guide."
In 1980, Perkins co-wrote and featured in the radio sketch show Radio Active, revised and adapted from the early Oxford Revue shows, and initially based around the comedy parody group The Hee Bee Gee Bees, consisting of Philip Pope, Angus Deayton and Michael Fenton Stevens. Prior to its leap from the revue to the radio, the production toured and appeared at the Edinburgh Festival Fringe, after which it was picked up by BBC Radio 4 for a pilot called The Oxford Revue Presents Radio Active. Radio Active, "which poked fun at the amateurishness of some local radio broadcasting," went on to run for seven series, and won a Sony Award. Perkins featured as a character called Mike Flex, a young cocky disc jockey.
In 2005 he cameoed in the fourth radio series of Hitchhiker's (The Quandary Phase), as the producer of the radio show Arthur Dent worked on. Essentially playing a fictional version of himself from the first series with a fictional version of writer Douglas Adams.
Perkins left the BBC in 1988, to become a director of Hat Trick Productions, an independent television and radio production company. Hat Trick's comedy programmes (produced for the BBC, ITV and Channel 4) included Have I Got News For You, Spitting Image, Whose Line Is It Anyway?, Drop The Dead Donkey, Harry Enfield's Television Programme and Father Ted, many of which won awards including Baftas.
Perkins meticulously read 30 new scripts every week, but "found himself culturally marginalised at the BBC," saying:
Perkins felt that the changes in how the BBC was run
"set the people that produce programmes in direct opposition to the people responsible for actually paying for and broadcasting them. "There have been occasions when you say, 'Let's just make a deal', knowing everyone is unhappy; where no one gets the budget they want to make their programme. There are people who are inspired by that, but I'm not one of them."
During Perkins' time as Head of Comedy, the BBC produced such hits as Jonathan Creek, The Fast Show and The Royle Family. Perkins also personally "persuaded David Jason and Nicholas Lyndhurst to star in a fresh series of the 1980s classic Only Fools and Horses, the first of which was screened at Christmas 2001."
In addition to starring in KYTV, Perkins appeared in small cameo roles in several of the comedy programmes he produced, including Father Ted, Operation Good Guys, One Foot in the Grave and The Catherine Tate Show.