They do not want the conduct of directors to face yet another serious scrutiny from a report by the great and the good, in the wake of the upheavals caused by the Cadbury Committee, and especially the Greenbury Committee on top pay.
The first brought a big increase in disclosure and in the power and influence of non-executive directors; the second took this much further, andmade remuneration committees of non-executive directors a new focus of power and influence on company boards.
Sir Ronnie Hampel, chairman of the newly formed Cadbury Committee Mark II, shows every sign of having taken on board what Adair Turner, the CBI director-general, calls industry's "corporate governance fatigue". He made clear that his work will focus on consolidation, not continuing revolution.
Sir Ronnie, the chairman of ICI, believes that it will take at least two sets of annual reports to see how Greenbury has bedded down. He has also sided with the CBI view that in some areas - such as smaller quoted companies - a certain amount of deregulation of the new rules might be desirable.
The Greenbury report was written in haste, under political pressure. Ever since, companies have been discovering awkward new side-effects that did not leap from the page when they first read it.
Geoff Lindey, a City fund manager who was the National Association of Pension Funds representative on the Greenbury Committee, found another yesterday in a speech to the association's autumn conference. The most important Greenbury recommendation, he believes, is that the remuneration committee chairman will attend the AGM to answer shareholders' questions on pay.
The corollary is that before they can justify high pay, companies will first have to spell outthe corporate performance objectives at which they are aiming. Very few now do. Mr Lindey says shareholders will ask questions, focusing managers' attention on performance in a way impossible before.
As this thought sinks in around British boardrooms, it will give new strength no doubt to the rearguard action against the report, which has already successfully delayed full incorporation in the Stock Exchange listing rules and led to a row about pension disclosure.
But there is a more fundamental reason why the corporate governance bandwagon has probably rolled about as far as it can go for the moment. Non-executive directors have exactly the same legal responsibility for stewardship of a company as executives. Yet the thrust of Cadbury and Greenbury has been to turn them into boardroom police, supervising executive directors on behalf of the shareholders.
This is where the Greenbury idea of a powerful non-executive remuneration committee, reporting over the heads of the rest of the board directly to shareholders, may run into the buffers. It gives the non-executives a separate status they do not have in law, and is thus an attempt to embrace surreptitiously some of the better characteristics of Continental two- tier boards without admitting they are a good idea.
As a fudge, this solution will work as long as nothing dramatic is expected of it. Such reforms are fine for well-run companies of the type in which Sir Ronnie and Sir Adrian Cadbury have spent their lives, and may even produce an improvement in the general performance and accountability of British business.
But they are more than likely to break down where they are most needed - at companies under strain, where boards are in disarray and businesses have problems.
Even at Cable & Wireless, hardly a corporate basket case, the supposedly influential non-executives do not appear to have grasped the extent of the row on the board until it was too late.
Perhaps the underlying reason business does not want to stir the corporate governance pot again is that the logical next step from the Cadbury and Greenbury reports would be to give legal reality to their attempts to create a special type of non-executive director-cum-police officer.
That might well lead to the imposition on an unwilling industry of a British version of the Continental two-tier boards. Business and the City are adamantly opposed to these, believing that they slow decisions and blur accountability between owners and managers.
The Labour Party recently came close, with a proposal that remuneration committees should contain a wholly independent director representing shareholders or employees. With an election looming, it is no wonder that business wants to put corporate governance on the back burner.
This is a serious tactical mistake, as Mr Lindey pointed out yesterday. Anything less than total enthusiasm for the present voluntary methods of improving the conduct of boards could provoke legislation and that could bring anything - even two-tier boards.