In some respects, the proposal, made increasingly publicly in the City, is a preposterous one. Certainly the idea that a bank of Barclays' pedigree should roll over and agree to be taken over by a company barely two-fifths its size would, coming from anywhere else, have been dismissed out of hand.
Yet the prospect of the Royal Bank of Scotland engineering what in effect would be a reverse takeover of the much bigger Barclays Bank has struck a chord, much to the annoyance of Sir Peter Middleton, the Barclays chairman and acting chief executive. When Sir Peter announced recently that he was axing 6,000 jobs, there was more than a suspicion in the City that the cost-cutting programme is in part defensive, designed to spike Sir George's guns.
Sir George, it ought to be said, is not everyone's cup of tea. Sometimes abrasive to the point of outright rudeness, his overtly Scottish separatist views go down like a lead balloon in the City establishment.
The feeling is mutual. Sir George has a notoriously low opinion of City fund managers, not to mention a good number of his competitors. Yet judged by the standards with which the City is supposed to measure the worth of a company and its management - the share price - he has certainly delivered. Since he took the helm in 1992, the Royal Bank of Scotland's share price has increased by eight times, and profits have risen by a compound growth rate of 19 per cent, more than any other UK bank including Lloyds and RBS's arch-rival north of the border, the Bank of Scotland.
The equivalent for Barclays was just 2.2 per cent, the worst performance of any major UK bank. Plainly there is a management job to be done at Barclays and Sir George reckons he is the man to do it. Perhaps unsurprisingly, Sir Peter Middleton has reacted to the suggestion of meetings with evident distaste.
Sir George must take his share of the blame for his lack of acceptance by the banking establishment. It is a club he has never been keen on joining. Fred Goodwin, whom he plucked last year from National Australia Bank, where he was a shoo-in for group chief executive, says: "I don't think even to this day George would call himself a Scottish banker. Mind you, I haven't come across many Scottish bankers in this bank."
Sprawled across a battered sofa in his cramped office in Edinburgh, one foot planted on a coffee table strewn with papers, Sir George is not one to stand on ceremony. "I hate pomposity," he says. Despite his recent knighthood, he prefers to be called plain George.
Diplomacy, too, has never been a strong point. Mr Goodwin again: "You never have to wonder what is in George's mind. It is quite refreshing how forthright he can be."
Sir George, a former aerospace engineer who ran the Scottish Development Agency for nine years, prides himself in not having been a career banker, and frequently makes his contempt for those who are a little too obvious for his own good. Yet he would say it is precisely this ability to come at things with a fresh eye and without the inherited baggage of a traditional banker that has enabled him to so dramatically transform the Royal Bank of Scotland in less than a decade, and by the same token uniquely equips him to run one of Britain's leading banks.
The Royal Bank today is a changed animal from the one to which he returned from his stint running the Scottish Development Agency in 1990, first as deputy and then chief executive of the bank.
A hostile takeover bid by the Hong Kong and Shanghai Bank in the mid- 1980s, which was blocked by the government on transparently political grounds, should have shaken the bank out of its complacency. It did not. Five years later it still took its position as a pillar of the Scottish financial establishment too much for granted. Board meetings resembled a dining club for the great and good of the Scottish elite rather than the decision-making forum of a FT-SE 100 company. Then disaster struck.
The low point came in 1992, in the trough of recession. With losses from bad debts mounting, Sir George, who had been pushing for radical change, got his chance. With the approval of the board, the newly appointed chief executive insisted the bank take a pounds 1bn bad debt charge and embark on a radical drive to cut costs and refocus on profitable areas. The bank declared a profit of just pounds 21m that year. In reality, the bank was heavily loss-making and possibly even bust.
Charterhouse, the merchant bank headed by Sir Victor Blank which had been acquired some years before as a folie de grandeur was sold off. With the help of McKinsey, the consultancy firm, the group began a systematic re-examination of what it was doing and how. The result - Operation Columbus - would turn the bank upside down. The immediate and most tangible impact was the loss of 3,500 jobs. But that was just the start. "Every single person ended up with a new job," Sir George says. The period was traumatic. He came in for criticism internally when market share in some traditional business areas started to fall. But within two years the results were starting to show.
Operation Columbus was about more than cost-cutting. Sir George wanted to shift attitudes within the bank so it embraced rather than resisted new business opportunities. He has few hang-ups about the fact that many of the innovations with which the bank is now most closely associated, like supermarket banking or Direct Line, were at least in part the result of other people coming to him. "You must never forget the importance of opportunism," he says. "Once you let it be known to people that you are prepared to consider new things, opportunities start to come your way." That, he says, was how the bank developed its strong position in acquisition finance, how the link-ups with Tesco and Richard Branson came about, how the bank ended up backing financier George Soros's bid for Greycoat, the property group.
For Sir George, the opportunity that may have opened up at Barclays has come late in the day. It may already be slipping away. Sir George's contract as chief executive expires next year. Merging with Barclays, he insists, wouldn't just be about filling the bank's vacant chief executive's chair. It would be about running RBS's proven management team right through the organisation.
He has nothing but praise for Fred Goodwin, who won his spurs managing the liquidation of the Bank of Credit and Commerce International for Touche Ross before moving on to the Clydesdale, where he slashed the cost-income ratio from more than 60 per cent to the low 50s in just three years.
Sir George says: "My father always said to me, `First-class men hire first-class men. Second-class men hire third-class people.' I have never been afraid to hire people who are better than me."
John Tyce, banking analyst at SG Securities, describes the fresh-faced Mr Goodwin as "the next Sir Brian Pitman" a reference to the chairman of Lloyds-TSB who is generally regarded as the most accomplished banker in Britain today.
Sir George has long relied heavily on Iain Robertson, one of several key staff who followed him across from the SDA. As head of the corporate bank he turned it from a business making pounds 200m a year to one which last year contributed pounds 500m, half of the bank's total profits. Below him is a tier of bright young Turks, including Benny Higgins, youngest general manager at Standard Life and now managing director of the retail bank, and Cameron McPhail, an MBA and economics PhD who ran Operation Columbus, now in charge of offshore banking. As one investment banker said last week: "Very few banks in the UK have such a strong management team. In comparison, once you get beyond Pitman and his chief executive Peter Ellwood, even Lloyds starts to look a bit thin."
At times the degree of devotion Sir George has inspired in those closest to him can seem dangerously like hero-worship. Others, even within the bank, can find him insufferably arrogant and bemoan the fact that since Bob Spiers retired as finance director there is no-one on the board to hold him in check.
Sir George relies heavily on his own instincts, seeing little point in the pursuit of intellectual coherence for its own sake. But his faith in the virtues of opportunism comes at a price. Critics accuse him of lacking clear strategic focus, and of simply buying anything that moves. Some say RBS, for a bank of its size, has its fingers in too many pies.
His failures on the acquisition front are not insignificant either. Over the years RBS has made overtures to the Woolwich, Scottish Widows, and the Nationwide, only to be rejected out of hand or seen valuations soar out of its modest reach. The one institution it thought it could bag - Birmingham Midshires, the building society - was snatched from its grasp by the Halifax. Detractors even now are calling his public attempts to ensnare Barclays ill-judged.
Supporters, not surprisingly, disagree. For one thing the acquisitions have all turned a profit. Howard Moody, another of Mathewson's fiercely loyal stalwarts from SDA days, says: "When Sir George went around the City years ago talking about a multi-brand, multi-channel strategy, they thought he was mad. Now everyone is trying to do it. The strategy has enabled us to acquire two million customers using other people's brands, far more cheaply than we could have done on our own. George can see round corners. He literally saved the bank."
Mr Goodwin, who since he joined the bank has forged what is obviously a very close relationship with Sir George, is also one of the most eloquent defenders of his thinking. Everyone in the industry - Barclays, NatWest included - is trying to imitate the Lloyds-TSB model: concentrating on those areas of the retail banking market where margins are currently high. He believes by contrast that there is virtue in hedging one's bets, particularly in a period of rapid change when bankers need to decide whether they should invest heavily in innovations like Internet banking without a shred of evidence that this is what their customers are going to want.
Mr Goodwin says: "Bankers are all talking about the future, when what they are trying to do is solve the problems of their past. Some are talking about it while in reality they are pulling the blankets over their heads. Others say they know exactly what the future is going to be. History says they are usually wrong. We fall in the category that says we don't know what the future is going to be. All we know is that it is not going to be the same. We would like to have as many options as possible."
In London for the group's annual results recently
Sir George berated the lack of ambition shown by the likes of NatWest and Barclays, supposedly the standard bearers of the British banking industry but who stand by as a wave of takeovers sweep the continental banking industry.
Friends describe Sir George as a closet Scottish nationalist, although a Scottish patriot might be more accurate. Mainly what irks him is the lack of ambition of those of his compatriots, who acquiesce in the inevitability of English domination. Yet here too there are signs of the defensiveness that often pops out when Scots feel they are being patronised by the English. The RBS top brass clearly feel the reluctance of the big City institutions to prod Barclays into listening to the case they believe they could make, is nothing more than a closing of ranks by the English establishment in defence of one of their own. "One thing I find irritating is this idea that I am a latter-day Attila the Hun sweeping through Hadrian's Wall to dismember an English bank," says Sir George.
He is also irritated by those who question his ability to run a large UK bank, because he has made his career in Edinburgh rather than London. Nor can he see why given planes, laptops, e-mail and mobile phones, a top British bank cannot be run effectively from Scotland.
City opinion in fact is far from universally hostile, but there is clearly a credibility gap to jump. One City analyst said last week: "RBS is a great story. The trouble is, that [RBS's story] is about cost-cutting in the context of revenue growth, Barclays is about revenue retention." Mr Goodwin will have none of that. "Anyone can buy cheaper pencils, but then you lose your best staff. The trick is to cut costs, and improve both top- line growth and quality of delivery at the same time. Nowhere is it written that Barclays cannot grow."
The cutbacks Barclays announced last week have already been dismissed as "too little too late". Sir George believes it will take a disaster of the scale RBS suffered in 1992 to force Barclays to change. But unless its shareholders can be persuaded otherwise, he and his team may never have the chance to prove that the lessons they learned are just as applicable to Barclays.