Indeed, if one of Ms Gleitze's descendants were to try to emulate her swim in 1999, two things would happen. An unknown assailant would dash up, just at the moment of triumph, grab her arm, uncouple the watch and disappear through the crowd. And an article would appear in the following day's newspaper saying how jolly naff it was for Mercedes to be wearing the thing in the first place.
What is it with Rolexes? In the last three years, street robberies in London have increased by 16 per cent. Since January this year, more than 160 timepieces have been whipped from the wrists of the rich and famous - and many of them have been the distinctive and sparkling Oyster Royal and Oyster Perpetual.
Former Page-three girl Jilly Johnson had her pounds 5,000 watch snatched as she sat in a Bayswater traffic jam. Caprice Bourret, the undies model turned singer, was relieved of her watch (and handbag and mobile phone) by a masked gang in Hampstead. Britt Ekland had her pounds 10,000 Rolex grabbed outside a supermarket in Chelsea. The chef Anton Mosimann was attacked in the street, outside his Kensington house, and his wife Kathrin's Rolex went west.
In June this year, Robert Robinson, the chortling radio quizmaster, lost his Oyster Royal when muggers beat him up in Chelsea. Only last week, the film director Ridley Scott's 94-year-old mother was burgled in Hampstead and her pounds 6,000 Rolex removed. More recently still, Anthea Turner, the television presenter, was sitting with friends in a Range Rover outside Stringfellow's nightclub when a man opened the door, lunged in, grabbed the eight-year-old daughter of millionaire businessman Ivor Jacobs, and forced him to hand over his pounds 20,000 Rolex Oyster Quartz Day-Date special.
The police are keen to stress the random nature of the attacks. Andy Trotter, the stylishly titled Head of Crime in Central London, said the muggers "are opportunistic thieves, they are disorganised and they will look around for likely targets. We see them wandering around, looking for targets, losing targets and finding another." Disconcertingly, different police reports variously suggest the bad guys are based in "south London", "the north west" of London and "east London".
All are agreed, however, that they travel to ritzier parts of town in search of jewel-dripping victims. The police have been tracking the watch thieves through surveillance cameras, and have sent plain-clothes officers on to the street, to stand around ostentatiously wearing Rolexes and acting dim. But why Rolexes? Surely their position as the top status symbol slipped years ago. Aren't they now about as up-to-date as an E-type Jaguar? Or have we missed something? Do they secretly possess a cachet on the international villainy market unguessed at by their watch-making rivals?
"For me, Rolexes are too flashy and too obviously trying to show your wealth on your sleeve - although there's a certain type of macho man who is perfectly at home with them," said Geordie Greig, the Tatler's new editor and arbiter of taste to the fashionable upper-classes. "If you're trying to show some style, you definitely wouldn't wear gold. A far better choice would be a Patek Philippe 5.35 with a silver or platinum case, a black strap and all its clever gadgets cunningly concealed."
The design guru Stephen Bayley couldn't disagree more. "I've been a Rolex wearer for ever," he said. "A steel Rolex is a perfect mechanism, self- winding, automatic, lasting for ever, utterly timeless. It's `the power of knowledge objectified', as Marx said about industry. It's very satisfying emotionally, poetically. It gives me pleasure every day. There was a moment, 10 years ago, when it seemed to be acquiring values quite alien to mine. But Rolex is still pre-eminent. Once you've graduated from a Timex, it's the only place to go."
Amid such discussion, it's easy to forget that Rolex started life not as a style object but as a serious chronometer. It was the brainchild of Hans Wilsdorf, a Bavarian-born horologist living in London. He and his brother-in-law formed a clockmaking firm called Wilsdorf & Davis in Hatton Garden in 1905, just as the first wristwatches were starting to appear on both sides of the Atlantic. They experimented with various models and gave them names: the Unicorn, the Marconi, the Rolco and Tudor - then, in 1908, hit on "Rolex" as an all-purpose word suggesting perpetual motion. When the First World War broke out, and all things German were suddenly anathema, Rolex became the company's name.
Wilsdorf was the first man to bring the technology of the testing laboratory (the screw-down winding crown, the automatic-winding rotor, the water-resistant cog) into a box strapped to your wrist. In 1926, he produced the first completely waterproof watch (a year before Mercedes went on her historic swim). In 1945, he invented the Datejust, the first wristwatch to show the date on the dial; then in 1956 trumped it with the Day-Date, showing the very-easily-confused traveller which day of the week he was in.
Rolex was less about telling time and more about precision - about being reliably accurate in extremes of altitude, depth, heat, cold, dryness and humidity. They were an absolute must for anyone venturing into a jungle, a desert, a trek to Antarctica, a scuba-dive or a transatlantic flight. The fact that 99.99 per cent of Rolex wearers would never be faced with any such eventuality did not dent their desirability. They were devices cognate with extreme elements and extreme behaviour, while being simultaneously emblems of perfect accuracy. That was their dual charm.
It was in the Sixties, though, that the Rolex image hardened into tough- guy territory. The black-faced Oyster Perpetual, with its huge white dots and red second hand became an emblem of sporty prowess and masculinity. Edmund Hillary's sidekick, Tenzing Norgay, wore a Rolex Explorer on the summit of Everest (Hillary himself wore a boring old Smith's). Donald Campbell had an Oyster on his wrist when he broke the land-speed record in Bluebird, the same model worn by Chuck Yeager when he broke the sound barrier in 1947. In the near-disastrous flight of Apolo 13, when the spacecraft was behind the Moon, out of touch with Houston, and the astronauts had to time to a split second the instant when they fired the scuppered rockets, Jack Swigert was gazing at the sweep hand of his Rolex GMT Master.
But it was James Bond who fixed the name in the public's mind as the essence of hard-man chic. Fleming was the first popular writer to pepper his text with real-life brand names, in an early literary version of product placement.
Along with Bond's favourite marmalade (Frank Cooper's Vintage Oxford) and cufflinks (Cartier) went the watch - "a Rolex Oyster Perpetual Chronometer on an expanding metal bracelet". Fully equipped - by Q, of course - the watch features, at different times in different movies, as a bullet-deflecting "intensified magnetic field" (which Bond uses to unzip the back of a woman's dress from the other side of the room), as a miniature buzz-saw and a garotte.
The Bond connection took the Rolex message to the ends of the earth - and 007's continuing appeal may partly account for the fact that Rolex watches remain phenomenally popular among Asian businessmen. In China, Hong Kong, Japan and Malaysia, a gold Rolex Datejust is still an instant and immediate sign that you're a big fat success. The best Chinese restaurants in Hong Kong throb to the combined tick of 200 Rolexes. In Yakuza [Japanese mafia] circles, the favourite tough-guy ticker is the Rolex Daytona - of course you've seen it: it's the one with three mini-clocks on the face, recording the passage of seconds, minutes and hours, accessorised by a pair of sunglasses and an amputation saw.
Look at the Rolex catalogue today, and you feel dive-bombed by luxury of a slightly ludicrous, old-fashioned nature. The serried ranks of 18- carat gold watches, with gold hands, gold faces and gold straps, many of them edged, trimmed and studded with diamonds, leave you feeling overwhelmed by excess rather than sick with longing. Who, bar some extra-flamboyant fan of the Emperor Bokassa, could warm to the Oyster Perpetual Day-Date with diamonds encrusted all round the bezel and set into the strap, let alone want to pay pounds 39,350 for it? Elsewhere in the catalogue, you can find some handsome models in steel and "white metal" that are an absolute snip at pounds 1,390.
As you read on it becomes clear that the point of all the assaults and muggings and burglaries by the Rolex Raiders is, pace the police analysts, more than random opportunism. We have to consider the possibility that, somewhere in Catford or Hoxton, a gang of sneering and criminal style- fascists are plotting to relieve the aesthetically-challenged and the insanely rich of their most conspicuous consumer mistake, like a tax on stupidity.
For it is surely self-evident that anyone who walks around, in the 1990s, with a guaranteed minimum of pounds 2,000 to pounds 20,000 in show-off yellow gold and look-at-me white diamonds lightly attached to his or her arm is taking part in an aggressive preening ritual - one that is now an object of wonder only to Pacific Rim millionaires and the nasty modern Dick Turpins who wish to emulate or serve them.