"No one has been rude, nobody has been unpleasant, people have tried very hard," Cleese said.
In an interview with The Daily Telegraph, the Monty Python star accused the BBC of needless interference, chaotic management and misspent budgets.
"No one has been rude, nobody has been unpleasant, people have tried very hard," Cleese said.
"And yet it's ..just been...bloody impossible."
The Human Face is a "major factual series" in which Cleese, famous for A Fish Called Wanda and Fawlty Towers, is to combine comic sketches with popular science to explore identity, beauty, fame and expressions.
Also taking part in the series are Elizabeth Hurley, Michael Palin, Pierce Brosnan and Prunella Scales.
Insights into the evolution of faces come from Sir David Attenborough, while scientists provide the facts and research.
Insecure
But according to Cleese the BBC lost its nerve and insisted on more facts and less humour.
Cleese quoted an e-mail he read saying: "We've had enough of Cleese's fooling about by now", as evidence.
"Well I don't mind them feeling that way," Cleese said.
"But why did they ask me to do it in the first place?"
Cleese, who has made dozens of very successful videos about corporate management techniques for his own production company Video Arts, specifically cited insecure BBC management.
"I think there's much more fear now than there used to be, much more fear of failure.
"When people get anxious they become control freaks."
He went on to blame poor management for the fact that the programme took "10.5 months to complete instead of five".
He said he had lost sleep as he tried to fight off interference and the insistence on putting in more factual content and less humour.
He added: "You go in and meet the head of BBC One and get an assurance about not dumbing-down.
"And then, of course a few months later, he's replaced by someone else you haven't met."
A BBC spokesman said BBC One controller Lorraine Heggessey had spoken to John Cleese several times and she and everyone at the BBC is delighted with the series and John Cleese.
"Like many series The Human Face has evolved since its conception, but viewers can be assured of a lively mix of popular science, psychology, culture and comedy," he said.
The Human Face begins with an episode about facial expressions on BBC One on 7 March at 2100 GMT.