Directors of the bank have their first opportunity to formally discuss the issues facing the bank in the wake of Mr O'Neill's departure, including the suggestion that Royal Bank of Scotland is keen to initiate discussions about a pounds 32bn merger.
RBS's claim to be the only bank that could realistically pull off a deal with Barclays at this stage was reinforced by comments by Peter Ellwood, the chief executive of Lloyds-TSB, at the bank's annual general meeting in Edinburgh. He said the bank was convinced that any merger with a bank the size of Barclays would be blocked by the regulatory authorities.
The prospect of a merger drove the two banks' shares higher yesterday. Barclays was up 25p at 1944p. RBS was up 19p at 1,444p, both against a backdrop of a falling market.
A hastily convened board meeting at Barclays on Monday endorsed the belief of Sir Peter Middleton, Barclays' acting chief executive and chairman- elect, that the bank should concentrate on finding a replacement and should not be panicked into a merger at this stage.
However, the meeting, which lasted no more than an hour, was specifically to address the terms of Mr O'Neill's departure and no substantive issues were discussed.
A number of key board members including Sir Nigel Mobbs, chairman of property company Slough Estates, and the senior non-executive were abroad and unable to participate fully in discussions.
Investment bankers said yesterday that they understood that the Royal Bank believed that Scottish Widows, the Edinburgh-based mutual life insurer, could be persuaded to join in a three- way merger. The attraction would be of a powerful savings brand.
"They have definitely talked about using Scottish Widows. That may be the card that wins the day," one banker said yesterday.
Barclays has so far responded coolly to suggestions of a merger deal. Barclays executives said yesterday: "We would not think of consolidation as a solution to our chief executive problem."
News analysis, page 17