The exhibition at Terminal 5 is based on the remarkable career of the airport's resident photographer Dennis Stone.

The best of times, as a passenger at Heathrow at least, probably came early on in the photographic career of the airport's legendary resident snapper, Dennis Stone. He'd started working there as a postboy at the age of 14 before picking up his camera full-time in 1965, by which time a new, state-of-the-art terminal, opened by the Queen, welcomed the world to Britain. As it happens, that building (which became Terminal 2) was deemed unsuitable for 21st-century aviation, and has since been unceremoniously flattened. In place of the narrow corridors that framed Stone's celebrity photographs of the time so naturally, today's arrivals plod along byzantine pedestrian superhighways that spin you around from aircraft to immigration to baggage to customs, then spit you out to face a barrage of faces. These, though, are neither adoring fans nor paparazzi: they are the minicab drivers fretting about how much the short-term parking is costing.

For the past 45 years of a career that has spanned seven decades at Europe's busiest airport – and which is currently being celebrated with a month-long exhibition at Terminal 5 – Stone has snapped the arrivals and departures of the planet's favourite celebrities, including Clint Eastwood, Frank Sinatra, Diana, Princess of Wales, Joan Collins and the Beatles. He is still working three days a week – but while the 78-year-old is not yet ready to hand over his airside pass, he may quietly have concluded that the good times (like the old Terminal 2 itself) have gone for anyone seeking allure and prestige in the increasingly dismal business of flying from A to B.

In the Fifties, landing in London really was a cause for celebration. This was partly because it elevated the passenger to membership of the tiny élite who could afford to buy an airline ticket (or who worked for a benevolent employer, usually a government, which would pick up the absurd tab). A ticket on the world's first jet route, a BOAC Comet from Heathrow to Johannesburg, cost £315 return – nine months' wages at the prevailing average British salary. And partly it was because the lucky traveller had survived the flight: fatal accidents afflicted UK airlines at a terrifying rate, with three losses in the first year of Comet alone. Today, of course, things have changed almost out of recognition. No UK airline has lost lives in a crash for 21 years. Air travel has become implausibly safe – and improbably cheap, with South Africa just five days' wages away for the average worker.

In 1969, supersonic civil aviation began – and, for the following 27 years, made Dennis Stone's job considerably easier. Concorde comprised the badge of exclusivity, and anyone emerging from that tiny, cramped white dart was automatically of interest to Stone and his flashgun. But the supersonic age ended seven years ago. Today, with the cost of entry to the six-mile-high club falling so low, and with the airport experience so undignified and stressful, any residual glamour has long been extracted from mass-market air travel. Heavens, even Joan Collins would be upbraided – or at least surcharged – if she tried to check in that famous collection of Louis Vuitton cases larger than a family car.

Stone's photographs tell a marvellous story of the changing times of travel – a boyish Clint Eastwood posing in front of the A1 bus that preceded the Piccadilly Line's Heathrow extension, Paul McCartney and family meandering unhindered across the apron in the days before terrorism homed in on aviation, and the attire of Sir Richard Attenborough confirming that the game was up in terms of dressing up for take-off.

As Stone celebrates a great career, the Spanish owners of Heathrow rightly want to make the most of the golden age of flying. But the future of aviation lies beyond the London Borough of Hillingdon: this summer, Dubai's hyper-modern new Al Maktoum International opened, and Heathrow has just been overtaken in terms of available aircraft seats by Beijing. Even through Stone's remarkable lens, the airport's own future looks hazy.