According to insiders, Mr Robinson, one of seven executive directors on the main board, was seriously contemplating leaving within days of last month's shock resignation by Peter Wood, the finance director. Another top-level departure would have undermined what little credibility still attaches to Andrew Buxton, the chairman and chief executive.
Mr Robinson's status as vice-chairman, along with Humphrey Norrington, places him equal third in the Barclays hierarchy, behind Mr Buxton and Sir Peter Middleton, the former Treasury mandarin who is group deputy chairman and chairman of BZW.
Mr Buxton came under heavy attack both in the City and within Barclays late last year for taking up the twin jobs of chairman and chief executive. At the start of this year, he reluctantly gave in to the criticism and agreed to split the jobs, seeking a chief executive outside the bank. But there are still critics inside and outside the bank who would like to see Mr Buxton replaced as chairman as well.
Sources claim that the 56-year-old Mr Robinson was close to following Mr Wood's example but was talked out of it by Barclays' top brass. Via a bank spokesman, Mr Robinson dismissed as 'nonsense' the notion that he threatened to resign. But insiders wonder whether he will stay on once Barclays has completed the now-desperate search for a new chief executive.
'If the new executive proves particularly aggressive, there must be questions whether Alistair will stay,' says one source. 'He has sufficient private means simply to go if he is fed up with the aggravation.'
At the moment, Mr Robinson reports directly to Mr Buxton. With the arrival of a new chief executive, however, he will be placed further down the hierarchy. Barclays claims this is unimportant since, in what amounts to a remarkable statement of the chairman's likely diminished position, Mr Buxton will take a strategic role and 'relinquish hands-on control of the group' to the new chief executive. It is not clear if Mr Robinson has ever sought the chief executive job or whether, like others, he is simply disheartened by the deteriorating atmosphere among senior executives at the bank, which announced pounds 2bn of bad debt provisions for 1992.
Mr Robinson became head of banking only two years ago. He is therefore untainted by the huge losses on loans made in the 1980s that have shattered Barclays' profits and undermined the credibility of Mr Buxton.
Amid the current turmoil, there have been suggestions that the Bank of England would like to engineer a link between Barclays and Lloyds. The notion is that a cross-shareholding - a temporary measure designed to surmount monopoly objections - would eventually lead to a full merger.