His most senior aide, Anson Chan, now serving as Chief Secretary and number two to the Governor, Chris Patten, has gone so far as to hint publicly that she might resign on a point of principle. In an interview with Newsweek magazine she said: "There might be issues that are points of principle, and, as a matter of conscience, you feel you cannot accept those decisions."
In the same interview she stressed that "Mr Tung is a person I can work with". However those close to the new order say there is something less than harmony, leading to predictions that the new Chief Executive will lose at least two of his two most senior civil servants within a year of assuming office. Mrs Chan aside, the other senior civil servants who might find their positions in jeopardy are Donald Tsang, the Financial Secretary, and Peter Lai, who heads the sensitive security department.
It is believed that Mr Tung was persuaded to keep all the heads of civil service departments, apart from the British Attorney General, by China's President Jiang Zemin. The reason was Mr Jiang's desire to preserve the stability of the Hong Kong government, in which senior civil servants perform roles undertaken by ministers in other systems. Mr Tung wanted to make some changes, but was told to bide his time.
The muttering coming from the civil service might be dismissed as normal at a time of change, but officials complain there is little dialogue with Mr Tung's circle, and little sense that their views will be taken into account. Accustomed to a well-established and orderly British bureaucratic system which operates on a collegiate basis, they are uneasy with a leader whose experience is of a hierarchical Chinese company where decision-making is autocratic and discussion minimal.
Mr Tung, a former shipping tycoon, "comes from a very different background", said Mrs Chan. "He has been, until last year, the head of a private organisation, a fairly low profile organisation, so, even though he has some understanding of the way government works, he doesn't have a deep understanding of how government machinery works."
The suspicion is mutual: Mr Tung himself likes to tell officials all the bad stories he has been fed about them, before insisting that he does not believe what he has been told. It shows, however, that the boss is listening to gossip, encouraging his subordinates to spread it.
Public comment on the tension has fallen to Mr Tung's controversial special advisor, Paul Yip, a businessman with close links to China-controlled organisations. Mrs Chan, he told Ming Pao newspaper, would have to get used to Mr Tung's way of doing of doing things.
Mr Yip added that Mr Tung was likely to be far more hands- on than any British governor, and would want to be involved in all levels of policy- making. "On current evidence," said a senior civil servant, "that would mean no decisions would be taken, or they would be very slow in coming."
Mr Tung has surrounded himself with a number of members of the old colonial order who were disenchanted with Mr Patten's democratic reforms, as well as some prominent left-wingers, but the people who really have his ear are fellow tycoons who pride themselves on being doers rather than thinkers. Some have been appointed to Mr Tung's Executive Council, or cabinet, whose meetings are said to be shambolic. Mr Tung gives little away about what he is thinking, and is loath to reach a decision in committee. The other members come to the meetings ill-prepared; they rarely read their briefs, and spend most of their time transforming what are supposed to be meetings of an executive into a mini-debating society.
The businessmen who advise Mr Tung want him to recreate the old colonial system, with an autocratic governor issuing edicts and getting things done with a minimum of discussion. Hong Kong, however, has moved on since those days, according to disgruntled officials. "You can't put the genie back in the bottle," said a member of the current administration. He is unlikely to thrive in the new order.