By demanding to meet Sir Michael Rake, the senior independent director and former boss of accountants KPMG, shareholders are demonstrating their lack of confidence in the bank's chairman Sir Marcus Agius.
"There are questions about the board to be answered," one shareholder said."The departure of Agius, at least in the short term, may be a better outcome than that of losing Bob," the shareholder said.
Another said: "The senior independent director needs to be called in and questioned."
Other sources confirmed that shareholders now want changes in the Barclays boardroom.
The attempts to bring Rake to discussions with investors came as a leading shareholder body called on Barclays to consider clawing back bonuses from directors in light of the fines. Diamond, for instance, has taken home nearly £100m since his pay was first disclosed in 2006, from a series of schemes dating back over a number of years.
Chancellor George Osborne told MPs on Thursday that Diamond had questions to answer and intervention at one point sparked a 16% dive in the bank's share price, although this is has since been pared back to a 10% slump to 175p.
David Paterson, head of corporate governance at the National Association of Pension Funds, said the board should look at clawing back bonuses and any long-term incentive awards made in past years. "We've had no response form the board on this," said Paterson.
He also said questions were being asked about whether the board was "properly informed" about the events that stretched back to 2005 and lasted until May 2009.
Shareholders had already been preparing to ask to meet Rake after the row over Diamond's £17m pay deal in 2011 and reports that the head of the remuneration committee Alison Carnwath had initially attempted to block the pay deal.
At the time, Barclays had issued a statement from that Agius saying that the bank encouraged "a full and vigorous debate" but insisted the pay deals were supported unanimously. The bank would not comment further on Thursday.
The penalties levied on Barclays are part of an international investigation involving a number of banks – including RBS and Lloyds Banking Group – into interest rates known as the London interbank offered rate (Libor) and the Euro interbank offered rate (Euribor). The two key rates play a key role in determining the cost of borrowing for households and companies.
Barclays was fined £59.5m by the Financial Services Authority and another £230m by the Department of Justice and Commodities Futures Trading Commission.
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