Broughton had told me about King’s passing just hours earlier, in his own characteristically low-key way. He hadn’t mentioned it until I was almost leaving, then said: “There is one more thing — Lord King died today, and I feel I should say something about that.

“The airline owes him a great debt, he took us through the privatisation process with Colin Marshall, and he and Colin got the service ethic into the airline. He will always be remembered at BA.”

Broughton, sitting in shirtsleeves in his London office, then gave a sombre nod to show that he had finished. Spare and economical, he didn’t need to say more.

But more will be expected this Tuesday, when Broughton, who is now BA chairman, conducts his first annual shareholders’ meeting at the airline. As a former boss of BAT, the tobacco giant, he knows all about hot seats.

Yet what does he know about airlines? He has never worked for one, nor headed a company so British. BAT, with its Lucky Strike, Kent and Dunhill brands, did most of its business abroad.

And what about the change of style? Both Lord King and Lord Marshall, whom Broughton replaced last year, shared passionate conviction and earnest, sometimes arrogant, drive.

By contrast, Fulham-born Broughton, lean and tousled, has a wry sense of humour and laid-back manner. He couldn’t seem more different from what’s gone before.

He will need that coolness this summer. Last week Broughton heard that the British Horseracing Board (BHB), where he also sits as chairman, had lost a crucial court case against bookmaker William Hill over data rights that could jeopardise the sport’s income.

Then at BA there’s the effect of the London terror bombings on bookings to assimilate (too early to tell, he says), and a new chief executive to bed in. Willie Walsh replaces Rod Eddington. That’s a lot on Broughton’s plate right now.

But if he’s feeling the squeeze, he doesn’t show it. Sitting in the seventh-floor London offices of the BHB — his life is a dash between BA’s Heathrow base and BHB’s West End eyrie — Broughton, 58, oozes sang-froid. With his rumpled face, shaggy hair, and gravelly voice, he looks like the kind of boss who would be happier out on the tiles than crunching numbers.

Broughton, however, trained as an accountant, ran BAT’s financial-services arm — before selling it — and has a reputation as a highly numerate organiser who gave BAT’s tobacco division back its confidence. After a 33-year career there, he says he can think of no company he would rather move to than BA.

Yet the airline has been through the wringer recently. Working in tough market conditions, it has had to cut back staff, and now faces restless unions, a steeply rising fuel bill, consolidation among competitors and pressure from environmentalists to curb airline growth. BA may be back in the black, posting increased profits of £415m for 2004, but there are problems all around.

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