Stephen Bayley, the latest adviser to quit, as creative director of the New Millennium Experience Company, said in a Sunday newspaper interview: "The whole way in which it is being run is pure East Germany. I get memos talking about the `creative task force'. It's awful ... and absolutely scary."
Mr Mandelson told the Press Association yesterday: "I have not been a dictator, but I have been decisive and I have got a grip on a project that was suffering from drift.
"The Millennium company has a first-rate chief executive and team working with her, but earlier last year the last Government was not providing the leadership they needed to do their job well.
"Mr Bayley's other remarks do not merit a response."
Mr Bayley had said that he could have created a stunning exhibition for pounds 100m, compared with the existing budget of pounds 750m.
Arguing that the project could turn out to be "crap", Mr Bayley said: "I don't like political interference and they don't like creative advice so it's completely undo-able from my point of view.
"There is a total mismatch between the creative impulse and political impulse. They won't take advice from me, Richard Rogers or Terence Conran, or any of their advisers."
Following Mr Mandelson's visit to DisneyWorld, he also said: "If Mandy went down to a voodoo sacrifice in Brixton tonight, he'd come back tomorrow saying, `We must have voodoo sacrifices in the Dome'."
Mr Bayley offered his resignation before Christmas, after working on the Greenwich project for six months. It was accepted last week.
Mr Mandelson said: "The Millennium project now has a strong sense of direction - the construction of the Dome and its contents are firmly on track and I am fully confident it will be a resounding success."
But Francis Maude, the shadow Secretary of State for Culture, Media and Sport, said there were already concerns that the success of the project had been jeopardised "by the high-handed and arrogant way that Peter Mandelson has run it. This concern is multiplied by Mr Bayley's resignation and his comments."
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