Sir John is still, you would guess, a keen learner. He never looks crosser than when he does not understand something. After I make a joke about Arnold-Baker doing his job too well - cross-promotion of BBC products is being investigated by the Monopolies and Mergers Commission - he scowls and appears confused. I explain and he laughs, but is clearly put out that he was not quick to catch the point.
After LBS his shin up British industry's greasy pole gained a fair momentum. Spells at General Motors, British Leyland and Massey-Ferguson led to Jaguar in 1980. Then fame, a knighthood, influence as a trusted supporter of Mrs Thatcher's, and finally BAA.
Why BAA? Simply the challenge, he says. It is multi-faceted: he loves the retailing side; he was intrigued by the property management aspect and saw parallels between the difficulties in managing a huge construction project like building Stansted and leading a car development team at a company like Jaguar. He is trying to work out new ways of discouraging cost overruns on the big projects. "It staggers me, for instance, that architects get more money if they overrun," he says. "We have to find some sort of bonus arrangement for reducing the cost."
And then of course there is his beloved market research. He underlines figures in his tables to emphasise their importance. No one can doubt their usefulness but, such is his enthusiasm, you wonder if there is a groan from his middle management every time he reaches for them.
The nub of it is that many now believe that he is better suited to BAA than he was to Jaguar. Most agree that his first year has gone well. A profits drop announced earlier this summer was little surprise after the ravages wrought elsewhere in the travel business by the Gulf war, and he has successfully given the company a face. Further problems are looming following the recent Civil Aviation Authority review of BAA's landing charges. A much tougher regime is proposed for the next five years which could hit BAA's income by up to 30%.
How long he will stay at BAA is another issue. He brushes it aside but there is uncertainty in the City as to whether he will eventually become chairman. New chairman Brian Smith, who takes over from Payne on August 1, is 62 and will presumably stay until retirement.
Sir John is certainly young enough, at 51, to look for other challenges. Some see politics as a possibility. He has always been close to the Conservative Party but his colours were pinned very firmly to Mrs Thatcher's mast. And a return to the car industry is hardly likely either, he says. As he points out, it is rare for car manufacturers to bring in people from outside senior executive positions. They normally prefer to breed their own.
Anyway, his own study of Napoleon should tell him that comebacks are not always a great idea. He had two Napoleon books on the go when we met: one a biography, another an analysis of his campaigns. Why two? "I have two houses," he replies.
Why is it that so many business leaders read about Napoleon? The unkind would say that they have delusions of grandeur. Sir John says that he enjoys reading about leaders with worse problems than his own. Then he offers me a tip: never mention Napoleon to Conrad Black. He is a great devotee, and liable to be "rather combative" over the minutiae of Napoleon's career.
It all reminds him, he says, of the time that he went to see Arnold Weinstock to ask for advice as to whom he should appoint as chairman when he was at Jaguar. "I asked him what the different roles should be of chairman and chief executive. He said it is very simple: a chief executive must be an absolute dictator but the chairman must watch him very carefully. When he turns into Napoleon then he has to shoot him."
Sir John laughs and looks rather pleased. He has presumably long since learnt how to handle his chairmen.
(Andrew Davidson is assistant business editor of The Sunday Times.)