The trouble was that until his signature was actually on the document he needed to avoid a press pack that had found out about his appointment, wrongfooting the Corporation and causing chaos in the BBC's publicity department. Reporters were already gathering at the imposing doors to Broadcasting House.
Then a BBC apparatchik had an idea - Mr Dyke could be smuggled into Broadcasting House via one of the wartime tunnels that runs between the BBC headquarters and neighbouring buildings, including the Langham Hotel.
And so, before he knew it, the soon-to-be director-general designate of the world's most respected broadcasting organisation was going underground, and being rushed through a dimly lit tunnel under the busy central London thoroughfare of Portland Place.
Soon he was in an anonymous office, accompanied only by Margaret Salmon, the BBC's director of personnel. There he was greeted by a BBC desk bearing a regulation Corporation vase of flowers, the contract and a piece of notepaper which some insider had already headed up with the words "from the director-general designate". He signed, and breathed a sigh of relief.
It had been a week of immense pressure for both Mr Dyke and the BBC governors, who had to decide whether they were prepared to ignore the criticism of the Pearson TV man's candidacy. Mr Dyke had given pounds 55,000 to the Labour Party (although the press had repeatedly reported the figure as pounds 50,000), and voices ranging from William Hague to The Times were saying this man could not possibly be given the top job in British broadcasting.
The BBC governors were split, and on Monday they decided to summon Mr Dyke to a secret location to quiz him one more time before making a final decision, even though he had already faced three gruelling interrogations. He was prepared. He knew that it would be no good simply to say "I can separate my personal life from my professional life, believe me". Instead he drew up a list of specific occasions on which, at his previous employers LWT, he had had to resist fierce political pressures from all sides.
The questions came thick and fast. Looking back on it, Mr Dyke says openly, "it helped that Christopher knew me as a journalist, and had worked with me in the past". He was referring to the fact that the chairman of the BBC, Sir Christopher Bland, was once chairman of LWT. Mr Dyke's relationship with Sir Christopher, like his friendship with the current director-general Sir John Birt, went back 22 years.
Mr Dyke and Sir John have played in occasional football matches together for much of that time. "The only problem with Greg is that he does not pass the ball enough ... even when you are in a goal-scoring position," says Sir John.
This coziness amongst the top men in broadcasting was, in itself, a problem for some governors. People like Baroness Young, the former chairman of the Royal Society for the Protection of Birds, the Rev Norman Drummond of the Church of Scotland, Heather Rabbatts, the Lambeth council chief executive, and Dame Pauline Neville-Jones, a former diplomat, were strangers to the clubbiness of broadcasting.
Even other board members closely associated with the arts, such as Sir Richard Eyre, the former National Theatre director, and Ranjit Sondhi, an ex-Radio Authority governor, had to think hard about the coziness. In the end they were won over by Mr Dyke's openness and journalistic enthusiasm. "I'll walk the floors of the BBC, find out what people are thinking," he told them. His style was clearly in sharp contrast to that of Sir John, who is often to be seen in strategy meetings, but rarely on the newsroom floor.
With the final grilling of Mr Dyke over, the governors met on Wednesday night in the "governors' dining room" on the third floor of Broadcasting House. The light-coloured room with its pale wood fittings was refreshingly less sombre than the "council chamber" where most difficult governors' decisions are made. While the frighteningly glowering portrait of Lord Reith dominates the chamber, the dining room is decorated with pretty impressionistic scenes of British cities.
The meeting was long and at times acrimonious. Sir Christopher persuaded the others that, whether or not Mr Dyke got the job, the outcome would be presented to the outside world as a "consensus decision". There would be no formal vote, thus denying the press the chance to play up the internal splits that had dominated the proceedings.
Across town in Westminster, whispering campaigns were underway that if Mr Dyke got the job he would not be allowed to take on the director-general's normal duties as editor-in-chief. Tories were suggesting that Mr Dyke could be a strategic head, while the BBC's head of news Tony Hall could act as the BBC's guardian of impartiality.
But the subject did not even come up over dinner in Broadcasting House. Sir Christopher had determined that since the governors had advertised for a "director-general and editor-in-chief" that was what they would appoint. In any case, it was highly unlikely that Mr Dyke would accept such a fudge.
At 10pm the governors were still arguing, but by 11.30pm it was clear that the decision had gone Mr Dyke's way. Even those who had strong reservations about his alliance with Labour realised that Mr Dyke was, in broadcasting terms, the strongest contender.
At midnight, Sir Christopher finally made the call to Mr Dyke to tell him he had won. Mr Dyke had spent the evening with his partner Sue having dinner at Bertorelli's restaurant in London's Charlotte Street. He was in the back of a chauffeur-driven car, heading home, when he received the message: call Christopher Bland.
The realisation that he had the job was an immense relief, the pressure had been enormous in previous weeks. "I was determined not to let it get to me, nor my family. And it didn't," he says. Even his critics had been impressed by Mr Dyke's coolness throughout. Halfway through the process he had gone to see his beloved Manchester United win the European Cup Final in Barcelona, and later he had coolly gone to the United States for a week to meet up with old friends from Harvard Business School.
After he spoke to Sir Christopher, he felt happy but exhausted. He did not celebrate, he just went home to bed.
The next morning the governors convened in Room B200 in the basement of Television Centre at Wood Lane in west London. They were due for their routine monthly meeting with the BBC's executive committee, which includes the BBC's top managers. The low-ceiling room is dark and airless, having no windows, and has a faint smell of old BBC tea. It was the beginning of a strange meeting. The governors could not tell the executive committee that the decision had been made, as Mr Dyke's signature was not yet on the contract. So normal business was done in the strangest of atmospheres.
One of the members of the executive committee was Tony Hall, a finalist in the race for director-general. He sat glumly through the meeting, realising that the governors' body language did not suggest that he had won. At the end, the governors did not stay for their usual lunch with the executive committee, and instead went off in a huddle.
Within hours, in the same building, Newsnight already knew what Hall did not - that he had lost and Mr Dyke had won. Some newspaper reporters also knew. It was inevitable that by evening, the BBC would be bounced into making an announcement.
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