I’ve made a discovery about what is buried under the swimming pools and basement conversions of wealthy west London. This booty is worth about £5m. More revealing, however, is another fact: this £5m was tossed away like small change tipped into a busker’s hat. It is not Nazi art, or plutonium that has been used to kill the enemies of Russian oligarchs. It is a fleet of diggers.

Beginning in the 1990s, buyers of London’s most expensive addresses began to feel a little hemmed in, even claustrophobic, inside their houses. Where could one take a swim, for example? Or watch a film on a cinema-size screen? Obviously, the idea of leaving the house to pursue such pastimes – and thus engaging with the human colour and spectacle that were once considered inextricably bound up with living in a city – was too ghastly to countenance. No, all pleasures had to be brought within the boundaries of one’s house, thus protecting the owner from the dangers of face-to-face interaction with normal civilians.

So, many of the squares of the capital’s super-prime real estate, from Belgravia and Chelsea to Mayfair and Notting Hill, have been reconfigured house by house. Given that London’s strict planning rules restrict building upwards, digging downwards has been the solution for owners who want to expand their property’s square-footage.

The challenge of adding new subterranean floors to London houses has become a highly lucrative business. The heavy lifting – or, in this case, the heavy digging – is usually contracted out to basement-conversion specialists. These firms discovered that it was reasonably easy to get a small digger (occasionally two) into the rear garden of a house on an exclusive 19th-century square. Sometimes they simply knock a hole in the wall and drive the diggers straight through the house. In other cases, the windows are so large that a digger can squeeze through without dismantling the bricks and mortar.

The difficulty is in getting the digger out again. To construct a no-expense-spared new basement, the digger has to go so deep into the London earth that it is unable to drive out again. What could be done?

Initially, the developers would often use a large crane to scoop up the digger, which was by now nestled almost out of sight at the bottom of a deep hole. Then they began to calculate the cost-benefit equation of this procedure. First, a crane would have to be hired; second, the entire street would need to be closed for a day while the crane was manoeuvred into place. Both of these stages were very expensive, not to mention unpopular among the distinguished local residents.

A new solution emerged: simply bury the digger in its own hole. Given the exceptional profits of London property development, why bother with the expense and hassle of retrieving a used digger – worth only £5,000 or £6,000 – from the back of a house that would soon be sold for several million? The time and money expended on rescuing a digger were better spent moving on to the next big deal.

The new method, now considered standard operating practice, is to cover the digger with “hardcore”, a mixture of sand and gravel. Then a layer of concrete is simply poured over the top. Digger? What digger? The digger has literally dug its own grave – just as the boring machines that excavated the Channel Tunnel were abandoned beneath the passage they had just created.

How many of these once perfectly functioning and possibly still serviceable diggers are petrified underneath central London, like those Romans preserved cowering in the corners of houses in Pompeii? Estimates vary. One property developer I asked reckoned at least 1,000; another put the figure at more like 500. In some of London’s newest luxury conversions, “sub-basements” are being tucked beneath the existing basement conversions. But developers are stumbling on a new kind of obstacle as they burrow deeper still: abandoned diggers from the last round of improvements.

On one level, the series of calculations that ends with hundreds of vehicles concreted underneath basements is entirely rational. On another level, it is a postcard from the front line of one of the craziest stories of our age: the global struggle to own elite London property.

In 1985, Michael Wood presented In Search of the Trojan War for the BBC. For many of us brought up in the 1980s, this was our first taste of archaeology. At times, the methodology seemed intriguing. Wandering around classical Asia Minor, the irrepressibly enthusiastic Wood would pick up a coin or trinket, or perhaps stumble on what might have been a foundation stone. He would then stare deeply into the camera and suggest something like, “Here, surely, lies the inner sanctum, the very essence of the seventh great Trojan civilisation.”

Three millennia from now, when Wood’s successors are excavating the dazzling ruins of west London, they will surely decipher a correlation between London’s richest corners and the presence of these buried diggers. The atrium of the British Museum, around 5000AD, will feature a digger prominently as the central icon of elite, 21st-century living.

What will the explanatory caption say? “Situated immediately adjacent to the heated underground swimming pool and cinema at the back of the house, no superior London address was complete without one of these highly desirable icons, sometimes nicknamed ‘the Compact Cat’. This metallic icon was a special sacrificial gesture, a symbol of deep thanks to the most discussed, revered and pre-eminent god of the age, worshipped around the world: London Property.”

Ed Smith’s latest book is “Luck: a Fresh Look at Fortune” (Bloomsbury, £8.99)