The song was the poignant end to 90 minutes of memories, poems and gags at a commemoration that was half service, half show. It was still strange, Dud said, to think that Pete had "kicked the bucket". John Cleese broke down as he gave the reading for the funniest man he ever met, who had been "extraordinarily free of ambition, envy and rancour".
The memorial was attended by legions of comedians from Cook's own generation and their successors. Michael Palin, Willy Rushton, Dave Allen, Mel Smith, Griff Rhys-Jones, Hugh Lawrie, Clive Anderson, David Baddiel - the congregation read like a Who's Who of comedy.
The troubled Stephen Fry was among the absent few, but in the order of service he paid homage to Cook's unmatched humour and poured scorn on suggestions that he was a "flawed genius" whose potential was never realised. No one, he said, should feel sorry for Pete because he remained in north London while Dud took Hollywood by storm. He had not been concerned with being a star.
In the formal tribute, the writer Alan Bennett, who appeared with Cook in the1960s revue Beyond the Fringe, said: "Even in his later years, when his talent for exuberant invention deserted him, I never heard him complain. He never complained about Dudley going on to Hollywood." When he revealed that Cook's only confessed regret was saving the broadcaster Sir David Frost from drowning in 1963, the congregation, Sir David among them, filled the packed St John's Church in Hampstead, north London, with laughter.
Richard Ingrams, former editor of Private Eye, said Cook saved the satirical magazine from closure in the early 1960s. After Cook's death in January, his widow, Lin Chong, allocated readers of the Eye - in which her husband had the controlling share - tickets for the service. Mr Ingrams said that columnist Auberon Waugh had written that everyone loved Peter Cook. "For once he spoke for all of us," he smiled. Cook had borne malice for no-one although he had once confessed to conducting "an irrational vendetta against the late Gracie Fields."
Mr Ingrams said that despite his popularity, Cook, thrice married with two grown up daughters, was a private man. He would turn up at the Eye's office unannounced after months of absence. "I don't think that many people did (know Peter) not even those of us who called ourselves his friends. He wasn't one to confide."
In middle age Cook became an "unlikely father figure" to younger comedians. And it was his kindness and professional generosity which appeared to lure so many to the service. "He was a tremendous help and encouragement to me when I received no encouragement from anyone," remembered Barry Humphries, alias Dame Edna Everage.
Cook mused about his own obituary when he made headline news after insulting Zsa Zsa Gabor on a chat show. Journalists' reliance on library cuttings. he concluded, would probably mean that his own death would be headlined "Zsa Zsa man dies." Dud said yesterday that Pete would probably not have turned up for the eulogy. But had he been there he would have been tickled by Harry Enfield's efforts to get past the usher who did not recognise him "from a hole in the ground" and by frail and unsteady Spike Milligan signing autographs while Barry Humphries protested, with mock horror, at his lack of taste, given the occasion.
And surely he might have smiled at the star treatment for the diminutive Dud, who was surrounded by camera crews, autograph hunters and adoring fans long after Pete's service was over.