Cynthia Carroll, the chief executive of Anglo American, has lost the confidence of leading shareholders who want her to consider merging the London-listed mining giant with its rival Xstrata.

Some big investors have drastically reduced their shareholdings in Anglo over the past year because of concerns over Mrs Carroll's leadership. They accuse her of overpaying for acquisitions and failing to deliver in the day-to-day management of the company.

“There are three reasons we sold: Cynthia, Cynthia and Cynthia,” one shareholder said. “It's nothing personal. We just don't think she has done a good job.”

The criticism comes as Anglo grapples with problems at De Beers, the diamond miner, in which it has a 45 per cent holding, which is in negotiations with bankers over $1.5 billion (£910 million) of debt scheduled to be repaid in March. Anglo shareholders are concerned that De Beers may need a cash injection. In February, De Beers borrowed $500 million interest-free from its three shareholders: Anglo, the Oppenheimer family and the Government of Botswana.

Anglo is also struggling to find a new chairman acceptable to the Government of South Africa, which has accused City institutions of racism for blocking the appointment of a black candidate.

These difficulties have prompted speculation that Anglo may be forced to consider a £45 billion merger with Xstrata if the Anglo-Swiss miner were to make an approach. Mick Davis, the South African chief executive of Xstrata, is coming under pressure from some of his own shareholders to pursue a merger but no discussions have taken place. Each of the miners is valued at about £22.5 billion.

Rebecca O'Dwyer, an Investec mining analyst, said: “Anglo would make a lot of shareholders happy if they did a deal with Xstrata. It is such a big job running Anglo that some shareholders think the only person who could do it would be Mick Davis.”

Anglo had lined up Sir John Parker, the chairman of National Grid, to head its board, but his appointment was blocked by the South African Government, which is the company's largest shareholder through public pension funds.

Fred Phaswana, the chairman of its Anglo Platinum subsidiary, was proposed as an alternative but was rejected by the City.

A senior adviser to the South African Government said: “There is a mixture of things going on and certainly maybe a whiff of racism on the part of the City in rejecting Phaswana.”

People close to the Anglo board rejected the allegation of racism and insisted that Mr Phaswana was not sufficiently well known to international shareholders.

The Anglo board is understood to want to avoid appointing a “politically correct” candidate. A possible compromise might be Nicky Oppenheimer, the chairman of De Beers. Sir Mark Moody-Stuart, the present chairman of Anglo, has agreed to stay on until next year.

Anglo shareholders are unhappy that Anglo axed its dividend without warning this year. Mrs Carroll said that this was done partly to fund the acquisition of MMX, a Brazilian iron ore operation bought for $4.4 billion.

A spokesman for Anglo said that many mining-sector acquisitions looked bad in hindsight but that the long-term value of MMX had not changed.

He added that investors had shown confidence in Anglo this year when its $3.7 billion bond issue was heavily oversubscribed.

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