But institutional anger has also spilt over to include the rest of the Barclays board, which shareholders fear is too divided to make important decisions or to find a solution to the bank's glaring management weaknesses.
'Buxton appears to be trying to hang on to something he should not be hanging on to,' remarked one leading shareholder on Friday. A substantial number of institutions have reacted adversely to the bank's pounds 240m loss and the dividend cut announced last week.
Despite Barclays' claims that shareholders still supported Mr Buxton, all but one of the institutions contacted by the Independent on Sunday wanted him to step down. Some said they thought Sir Peter Middleton, the deputy chairman, should take over.
One shareholder was prepared to see Mr Buxton continue as chairman as long as a reliable chief executive is appointed. However, there is concern that board divisions may be stalling the appointment because several senior executives, including Sir Peter, appear to be unwilling to give up any of their responsibilities to a new chief executive. Barclays is refusing to say how soon it hopes to make an appointment.
'Sir Peter Middleton seems to be against Mr Buxton but can't seem to dislodge him,' said one investor. 'Why is the board doing nothing? And what are the non-executives up to?'
Most shareholders are alarmed that there appears to be no one to represent their interests on the Barclays board. Many have completely lost confidence in the ability or willingness of the non- executives to intervene in events. Some shareholders are expected to ask for a meeting with the non-executives, who include Sir Nigel Lawson, Sir Denys Henderson, chairman of ICI, Sir Nigel Mobbs, chairman of Slough Estates and Sir Derek Birkin, chairman of RTZ.
Barclays shares rose sharply on Friday by 16p to 408p after active buying, particularly from the US, on recovery hopes. But some investors are already worrying about next year's results, which Barclays indicated were likely to be little better than this year's. 'You have to worry that the interim dividend will be cut next year, especially if Barclays is inadequately provisioned against bad debt,' said a shareholder. Some analysts believe the bank is under-provisioned by about pounds 1bn.
Mr Buxton will have to meet these criticisms face to face with shareholders at a series of road-shows over the next few weeks. The presentations in Scotland were to have been made by Barclays' investor relations officer, but Mr Buxton himself is now due to go along following the outcry over the bank's performance.
The chief problem for Barclays is the issue of its management. Despite the larger than expected loss, the City was generally relieved when the bank decided to cut its dividend to protect its capital position.
Although Mr Buxton said last week that the careers of some managers had suffered as a result of poor lending decisions, he gave little indication that he thought he or any other board members involved in setting the bank's lending policy were responsible for the huge losses.
His attitude is likely to cause a further drop in staff morale, which is already low following thousands of job cuts and poor performance.
To add to its tale of woes, Barclays is also lead bank to First National Finance Corporation, which revealed last week that it is in breach of its banking covenants. As a result, a pounds 150m bank refinancing package has collapsed.
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