The feng shui-inspired huge glass construction certainly is impressive with its indoor olive grove, running brooks and French stone floors. The building has a restaurant, coffee bars, a bank, an in-house florist - and even a small branch of Waitrose. In summer, staff can lunch amid wild flowers or on the pebbled banks of the lake in the adjacent park, the biggest to be built in Greater London for a century.
During our chat in the expresso bar, Ayling jumps up on several occasions to greet staff he recognises.
Jacketless and relaxed, Ayling was on good form, if not a little tired after what had been a comparatively good week for the airline chief, who seems to fly into turbulence as regularly as his pilots. On Wednesday, arm-in-arm with his mate Tony Blair, he announced a multi-billion pound pact with the European airplane manufacturing consortium Airbus to buy 59 new short and medium-haul aircraft, with options for another 200.
Hitherto, the company had only bought planes from Boeing, the arch-rival of Airbus. Ayling insists Airbus was chosen because it offered a better package both in terms of price and all-important after-sales service, including free maintenance.
That did not stop the leader writers from firing off accusations of narcissism and political patronage. Ayling is, after all, New Labour's favourite businessman. He is a personal friend of Tony Blair and celebrated his 50th birthday party two years ago with the Home Secretary, Jack Straw.
Ayling, who once worked under Norman Tebbit at the DTI over BA's privatisation before moving to the airline, heads the organisation responsible for corporate sponsorship of Peter Mandelson's pet project, the Millennium Dome.
Newspapers pointed out it is in his interests to stay sweet with the European Commission, a great friend of Airbus. Negotiations are currently under way between BA and the EU regulators on how to implement the concessions they demanded in order to approve Ayling's grand plan to link up with its former arch-enemy, American Airlines.
But after a two-year competition probe, Ayling, who initially refused to accept Brussels' jurisdiction over the alliance, has mellowed, at least temporarily, in his attitude towards the EU. Besides, say his aides, he has always been pro-European.
Brussels wants BA and AA to relinquish frequencies on a number of transatlantic routes to give the competition a chance, and to relinquish up to 267 take- off and landing slots.
To complicate matters, a row is brewing between the Commission and BA, backed by his friend Mandelson, as Secretary of State for Trade and Industry, over whether those slots can be sold to competitors for up to pounds 2m a piece.
"Slots are legal rights, and as is the case of all legal rights, they have a value - and can be legally bought and sold unless there is a prohibition. And there is no prohibition," says Ayling.
Sale of slots aside, though, is it still worth carrying on with the deal? "If the value of the alliance is less than the cost of the conditions, then obviously we won't proceed."
Surely BA, which received the conditions from Brussels last July, must have done its sums by now? "You've hit the point where I'm not going to say any more on the subject because anything I say will be disadvantageous for BA and advantageous for other people," says Ayling. "Certainly we are not yet in a position where I am happy with the conditions that are proposed."
Even so, it is still hard to tally the serene surroundings of BA's feng shui HQ, with the angry scenes at Heathrow last summer when BA stewardesses marched against his plans to slash pounds 1bn from company costs. Their strike action grounded planes, the true cost of which has still to work its way through to the company's bottom line.
Even the City took umbrage with Ayling's confrontational approach toward the unions who branded him a "Macho Man" of the Murdoch ilk.
Ayling, who like Margaret Thatcher is the child of a grocer, albeit a Labour-voting one, is a difficult man to fathom. He has also been accused of arrogance. When he swapped the Union flag emblem on the tailfins for the now famous multi-ethnic designs, some angry shareholders believed he was mad.
Yet face-to-face, the elegant 52-year-old comes across as cautious, maybe a little shy, even though he looks you straight in the eye. He still lives in modest Stockwell in South London, and spends his weekends in Wales so he can be with his oldest son, who has Down's syndrome and spends the week in a special centre there.
He speaks in the measured tones of a skilled lawyer, and his answers can be clipped. But he is anything but macho.
He reddens slightly when I inquire about the state of industrial relations at BA now. That morning he had been conferring with the troops at Heathrow. "The atmosphere was better even than I thought it would be." he says. "There has been a big climate change at BA over the year and a recognition by everyone that the cost-efficiency programme is necessary."
BA has already achieved half its target to slash pounds 1bn off its costs by 2001. If all goes to plan, it should have made savings of pounds 750m by 2000, with just an extra pounds 250m to the finishing line.
"We must now work together and put people management at the top of our agenda to maintain our very high standards of the future," says Ayling.
The City is still far from convinced. "That's the image he's now trying to project: New Labour, new building, new friendly guy," said one cynical City insider.
The City's frustration with Ayling is due largely to the performance of BA's share price, which has fallen more than 10 per cent this year. The cost of the strike is one negative, but other airline stocks have also dropped amid fears that airlines will be prime victims of the global economic crisis.
Mention the share price and Ayling is quickly on the defensive. "The treatment of airline stocks, certainly our stock, has been a knee-jerk reaction to the world economic situation. Our industry is affected, but not to the extent of the reduction in the value of the company that we see," he says.
Nor is the macro economic outlook as bad as the pundits make out. "I certainly don't think it's dire and we expect to see improved results for this year," he says, pointing to the strong recovery in mainland Europe.
Indeed BA posted a 77 per cent rise in first-quarter profits, although it was less than the markets had been hoping for.
So what would be the best news Ayling could hear at this time? "To continue to see smiles in the company. You don't see a lot of unhappy people here," he replies.
Let us hope, for his sake, the smiles are not just for his benefit.