Cook, a groundbreaking satirist who died in 1995, was known for his 1960s and 70s double act with Dudley Moore in shows such as Not Only... But Also.
He beat John Cleese, who was second on the list for a Channel 4 show, with Woody Allen, Eric Morecambe and Groucho Marx following in the top five.
Tommy Cooper, who was sixth, topped a separate fans' poll by Comic Relief sponsors McCain, published on Saturday.
The Channel 4 top 50 list, also revealed on Saturday, had no place for Cook's comedy partner Moore.
Modern comedians paid tribute to him on the show. Arthur Smith said: "He had talent oozing out of him and he hardly had to exert himself as he was so brilliantly funny.
"He influenced a whole generation of people - even now he's spoken of in terms of awe."
Double acts Laurel and Hardy and Vic Reeves and Bob Mortimer had joint places in the top 10, where they were joined by Billy Connolly and Richard Pryor.
Modern TV satirist Chris Morris was in 11th, followed by Tony Hancock, Bill Hicks, Peter Sellers and Steve Martin.
Other current stars in the top 50 included Steve Coogan at 17, Eddie Izzard at 19, Paul Merton at 20, Peter Kay at 22 and Rowan Atkinson in 24th. The Office creator Ricky Gervais could only make 49th place.
The only females in the top 50 were Victoria Wood at 27, French and Saunders in 31, Joan Rivers at 40 and Joyce Grenfell one place behind.
In the McCain poll of 4,400 fans, Eric Morecambe and Peter Sellers followed Tommy Cooper, with Peter Cook in 10th.
