And it's true: you could play badminton in there; even, I suspect, indoor tennis. It's a stonking great room, overlooking the Prime Minister's garden, painted in a rather bilious yellow. Heseltine, I gather, used to sit at his desk right at the far end, his back to the door, while his visitors trekked across the floor to him - only turning to face them at the last minute.
They had to sit on low sofas, while he was on a tall chair far above them. Cabinet colleagues found that they had to perch on the very edge of their seats, like nervous job interviewees. But once, apparently, John Gummer gave up, leant back - and fell asleep.
Come the Mayday revolution, Hezza's throne room became a meeting hall (John Prescott has to make do with a much smaller office, which he rarely visits). I was there as one of a small group being consulted by ministers and senior officials on how to improve the practice of government, in preparation for a White Paper.
Heaven knows why I was invited. I spent most of the time listening to real experts - people such as the academic Ben Pimlott, the trade union leader Rodney Bickerstaffe and practitioners from local government - only piping up over deregulation, on which I have sometimes written. However, the meeting also touched on plans for electronic government exclusively reported in the Independent on Sunday this month.
Early signs are that the plans - drawn up by David Clark, the Chancellor of the Duchy of Lancaster - are popular. An NOP poll suggests that more than three-quarters of Britons would welcome computer kiosks in libraries and shopping centres to dispense government services - such as providing vehicle and television licences - a likely early development.
You May have heard little of David Clark - certainly far less than of his nominal deputy, one Peter Mandelson. Neither man would qualify as a lily of the field - but it's Dr Clark who does the toiling while Mr Mandelson does the spinning.
He is that rare beast at the top of politics, an honest, unflashy grafter. As Labour's agriculture spokesman he investigated BSE, when few cared, and reported on the shocking state of abattoirs. As shadow defence secretary he took the portfolio - long Labour's Achilles' heel - off the political agenda, while championing servicemen with Gulf War Syndrome. In his present job he is supervising the creation of the Food Safety Agency, pushing plans for a Freedom of Information Act (with the backing of the Prime Minister, but the determined opposition of some Cabinet heavyweights), and leading the drive for better government. He's worked hard at home, and personally investigated best practice overseas.
Which makes it a bit odd that there are constant press reports that Tony Blair is about to replace him with Mr Mandelson, whose only hands- on project is the Government's greatest embarrassment - the Millennium Dome. If they are true, it will tell us quite a bit about the future direction of the Government, signalling to ministers, and wannabes, that style is more important than substance. If they aren't - who could possibly be talking the story up?
As The meeting began, we were assured that Hezza's old room was the most secure from bugging in Whitehall. Which reminded me of the time a senior civil servant in the Ministry of Defence demanded an inquiry into who had leaked information about a story I was working on. Eventually a junior spook came into the official's room witha tape recorder and pressed the play button - to reveal the mandarin's own voice doing the leaking. To adapt the old tag, who bugs the buggers?