Wanted: One senior executive to oversee the most exciting civil engineering project of the century.

But far from being swamped with applications, the group looking for a new chairman is struggling to drum up any interest at all. Britain's captains of industry are distancing themselves from the headhunters, much to the embarrasment of Margaret Thatcher and her government.Plans to build a fixed link between England and France are now in deep trouble, thanks to board room differences within Eurotunnel, the Anglo-French consortium which won the contract to build and operate a twin bore rail tunnel under the English Channel.

As efforts continue to find a new British co-chairman of Eurotunnel well ahead of the next fund-raising exercise, the first rumblings of doubt about whether the link will ever be built at all have started to appear in the British press. Mrs. Thatcher, who is closely identified with the project

because of her enthusiastic support for a Channel tunnel, is reported to have discussed with senior colleagues ways of containing the political fallout should the whole scheme collapse.

Embarrasingly for the government, the problems now being faced by Eurotunnel are not of a political nature but resistance in the marketplace. Mrs. Thatcher, who sets such store by free market forces, has insisted all along that no public money would be invested in the project and that all necessary financing had to be raised in the private sector. But whereas recent privatizations in the United Kingdom have proved there is no shortage of cash where investors can scent the chances of short-term profits, there is still great reluctance to tie up funds in long-term ventures.

A share placing last October to raise 206 million ($300 million) very nearly flopped when City of London institutions dragged their feet, discouraging investors in the United States and elsewhere. The money was only raised after a few persuasive phone calls to key fund managers from the Bank of England.

But a much larger equity offering of 750 million is planned for this summer to finance the next stage of the project. While the French members of the consortium are confident of coming up with their share of money, the internal squabbling over who should run the British side of Eurotunnel is likely to scare off investors unless the difficulties are resolved very soon.

Several months of quiet misgivings about the leadership qualities of the British co-chairman of Eurotunnel, Lord Pennock, have given way to well- publicized board room rows in recent weeks. And as the crisis deepened, Lord Pennock, a director of the U.K. merchant bank Morgan Grenfell, found

himself caught up in other problems.

Morgan Grenfell, as adviser to the brewing concern Guinness, is involved in government investigations into alleged illegal share dealings. During recent internal management restructurings in the wake of the Guinness scandal, Lord Pennock accepted new responsibilities at Morgan Grenfell without advising his Eurotunnel colleagues who complained bitterly that he would have too little time to devote to the tunnel project.

Lord Pennock has now confirmed he will resign from the position of Eurotunnel co-chairman just as soon as a replacement can be found, and the search is now on for a more charismatic figure with a higher public profile who can revive Eurotunnel's battered image and get the project back on track.

The government's first choice would be Sir Nigel Broackes, the dynamic chairman of the construction and shipping group Trafalgar House who is already a Eurotunnel board member. However, his nomination is being resisted by the five other construction groups involved in the project who fear Trafalgar House may land more than its fair share of the lucrative contracts in the offing.

Sir John Harvey-Jones, the ebullient outgoing chairman of Imperial Chemical Industries, has turned the job down. Others who have been sounded out include Sir Michael Edwardes, the chairman of Chloride Group and former head of British Leyland; Sir Jeffrey Sterling, chairman of P&O, and Sir Ian MacGregor, the former head of the National Coal Board.

With the French looking on in bewilderment as yet another attempt to link Britain with the continent stumbles, the government is in a race against time to rescue the project which would cost it dearly in terms of political loss of face should Eurotunnel fail to win back the confidence of investors and prove unable to fund the $4 billion project.

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