The improvements are mostly to the cabin area which was beginning to have a 'tired and dated image', much to the displeasure of its elite clientele. The new, all-grey livery will be its last as the aircraft is expected to survive in service only until the early years of the next decade.
The aircraft, which was intended to usher in an era of supersonic air travel, is approaching old age, having first flown commercially in January 1976. The revolution it was supposed to inspire has long been abandoned.
Apart from Concorde, air travel is still subsonic and is likely to remain so well into the next century, if not forever. As Mike Ramsden, editor of the Royal Aeronautical Society's magazine Aerospace, put it: 'Concorde was Europe's answer to America's Apollo project to put a man on the moon. It was a way for the British and French to cock a snook at the Americans, to show that we had the edge on technology and it was a way to develope our entente with the French.'
The cost of that impudence has been enormous. The project never repaid a single penny of its development costs of around pounds 1.1bn, nearly 10 times that sum in today's money, because of a series of fundamental mistakes. The most important of the errors was the failure to realise that the noise - not only the sonic boom but the ruckus on take-off which, despite some improvement, still sets off car alarms in airport car parks - would arouse so much opposition.
The blunder was understandable. The project was conceived in the late Fifties when propeller aircraft still ruled the skies. It was only by the time of the first test flight in March 1969 that the anti-noise lobby, which first came to the fore in New York, was becoming a powerful force - for Concorde, a deadly one.
As Mr Ramsden recalled, Concorde became a pawn in the fight between those who believed in human beings' ability to conquer all through technology and those who felt that such developments were threatening the future of the planet. With Concorde, the latter won through.
Airlines such as Qantas, PanAm and TWA had taken up options but on one black day in February 1973 they decided, simultaneously, to cancel and what, initially, had been 58 options by foreign buyers became zero sales. Only Air France and British Airways, both state-owned, whose governments had jointly sponsored the project, would ever put them in service.
There were other problems. The range, at around 4,000 miles was too short to cover any of the lucrative routes, apart from the Atlantic. Fuel consumption, too, was so high that with only 100 passengers, the economics were impossible to reconcile.
The oil price shock of 1973-74 was the last straw, although BA had already discovered there was no market. A former BA executive recalled: 'We found out that the potential market to Melbourne, with fares at first class rate plus 20 per cent, which is what was needed to make a profit, was all of 11 people per week. It was obviously impossible.'
In 1976, the first two Concordes took off simultaneously from London and Paris on their inaugural flights. Over the next few years, British Airways and Air France built up a network of routes encompassing Bahrain, Rio de Janeiro, Dakar, Mexico, Singapore and Dallas, as well as New York and Washington. But with the exception of the transatlantic routes, they all lost money, even without taking into account the aircraft's capital costs.
By the early 1980s, calls to abandon the project were mounting on both sides of the Channel. The clamour reached a crescendo when a select committee found that it would be cheaper to scrap the project.
BA fought back, encouraged by the supporters of the project, who had, as one former executive put it, 'a schoolboy enthusiasm for Concorde'. The politicians did not dare go against the wealth of feeling, and saved Concorde by the simple expedient of giving the seven aircraft to BA, writing off the nominal pounds 32m charge for each aircraft.
BA scrapped the route network it had developed, the Atlantic crossing apart, and put its faith in charters, the favourite being the quick supersonic burn-up round the Bay of Biscay. But essentially the plane became an irrelevance, except as the flagship aircraft used by people everybody had heard of.
BA began to make a modest profit out of Concorde but with privatisation the beneficiaries are now its shareholders. Today, apart from the charters and a handful of winter flights to Barbados, BA flies twice daily to New York and three times a week to Washington, although this route is now a loss-maker.
With only 34 flights a week shared between six aircraft - the seventh is used for charters - the engineers may find a way of prolonging Concorde's life into the early 21st century but it may not be viable to do so.
Meanwhile, the debate about whether it was all worthwhile continues. There have been spin-offs, as Mr Ramsden pointed put. 'Concorde gave us carbon brakes and helped give Europe the lead on 'fly by wire' technology which was introduced by Airbus five years ago - Boeing is still three years away from it . . .'
The biggest complaint of the anti- Concorde lobby is that it wrecked the British aerospace industry. Other more viable projects such as BAC's 3- 11, a wide-bodied jet for which there had been 50 orders, were scrapped because Concorde ate up all available research and development money. Without Concorde, Britain may have been able to keep its aerospace industry for a decade or two. Instead, it went down a technological dead-end.