Though the board meeting may not decide the issue today, the level of shareholder concern is such that Sir Desmond's tenure as executive chairman looks almost certain to end before Christmas. Soundings of City investors were taken last week by Sir Peter Middleton, chairman of BZW and a United non-executive director. Sir Peter was left in no doubt about the unhappiness over Sir Desmond's role in the shock ousting last month of Brian Staples as chief executive.
As one institution put it yesterday: "We'd prefer it if he left now. But you have got to be pragmatic about these things. If he goes in three months' time it's still a lot better than 2000." United is also under intense pressure to replace Sir Desmond with a non-executive chairman, avoiding future conflicts between the chairman and chief executive.
For Sir Desmond the loss of shareholder confidence so soon after the sacking of Mr Staples has a bitter irony. Though Mr Staples' reputation in the City was somewhat mixed, it was the exposure of the machiavellian goings on inside United's Warrington and Mayfair headquarters which cast doubt of Sir Desmond's own position.
His proud championing of United's "Progress with Responsibility" initiative at the group's results earlier this summer took on a hollow ring as stories of frequent rows between the two executives became public. The news that Mr Staples had left his partner to live with Anne-Marie Smith, Sir Desmond's secretary, did little improve matters.
With hindsight the reign of King Des, former head of Littlewoods and perhaps the most influential figure in affluent North-west business circles, began to falter more than a year ago. United launched a controversial long-term share bonus plan which could give executives payouts worth up to 87 per cent of salary. At the same time Sir Desmond received a 21 per cent basic pay rise, taking his salary to pounds 310,000. Even the normally relaxed Association of British Insurers came out publicly against the scheme, suggesting several big investors thought it was "over generous and over complex".
"You could say Des did more to highlight the executive pay problem than anyone else, except perhaps Cedric Brown at British Gas. He single-handedly exposed the issue of long-term share bonuses and showed the lack of teeth in the Greenbury proposals," said one big shareholder yesterday. It was also the last thing the utility companies needed as they stepped up their fight against Labour's proposed windfall tax.
By the group's annual shareholder meeting in July 1996 Sir Desmond had been crowned "king of the fat cats," taking the accolade from a no doubt relieved Mr Brown. Ian McCartney, Labour's employment spokesman, even turned up to hold a mock coronation ceremony on a protester wearing a pantomime catsuit for, as he put it, "services to fat cattery".
Though executives lost the vote on a show of hands, reflecting the anger of small investors, they won the reluctant backing of City institutions. The scheme was eventually amended after intense shareholder disquiet, but the damage had been done.
The taunts took on a sinister complexion when, in June this year, Sir Desmond's Cheshire home was the subject of an arson attack, with the kitchen set alight. Sir Desmond and his wife were out at the time. An anonymous telephone call to police later claimed it was the first in a series against "fat cats".
Meanwhile Sir Desmond was forced on the defensive when the company announced the losses of pounds 90m on a municipal sewerage contract in the Thai capital, Bangkok. The whole board waived short-term cash bonuses for last year to reflect the difficulties.
Mr Staples, with his experience from construction group Tarmac, was handed the task of sorting out the mess, despite the fact that he had not joined United when the contract was first signed. Institutional investors again cited this as a sign of the apparent inability of senior executives to work together.
If Sir Desmond does agree to step down then he may look back on the formation of United Utilities at the start of last year as his major achievement. The pounds 1.8bn contested bid by North West Water for Norweb created a multi- utility leviathan which left King Des in control of water, sewerage and electricity across a huge chunk of the densely populated North-west.
Yet his bold pledge at the time - to boost shareholder returns through restructuring the combined operations - has a different tone 18 months on. Institutions and analysts alike now complain of United's "dramatic underperformance" and `lack of direction" questioning what Sir Desmond has done to justify his generous pay package.
This looks like being one battle King Des cannot win.