Think the swimming pool and tennis court in your garden make you pretty smart? Well, sorry, but that's just so 20th century. These days, if you want to keep up with the oligarch next door, you put your play things under your London house.

Londoners have used their underground space for a long time. Winston Churchill had war rooms, Joseph Bazalgette dug sewers, and the capital's cheerful commuters have enjoyed underground rail transport since 1863. In the last 20 years, however, advances in building and lighting technology have accelerated the rise (or, more accurately, descent) of a new underground trend: the mega-basement.

Big British houses have traditionally used basements as dank wine storage and dungeon space. Now, however, it's possible to create several floors of light, spacious rooms underground. These might include, at the top end, ballrooms, galleries and swimming pools.

These mega-basements are serendipity for the drivers of the super-prime property market. London's tiresome planning laws prevent you from knocking down your 17th-century palace and replacing it with a more functional skyscraper. This has long frustrated the expansion plans of men and women with a spare hundred million pounds or two.

Now, perhaps envious of steel man Lakshmi Mittal's jewelled subterranean Kensington swimming pool, other London-dwelling tycoons such as Russian oil billionaire Leonid Blavatnik, estate agent Jon Hunt, and the Sultan of Brunei, as well as celebrities such as Take That's Mark Owen, are planning and building underground lairs that mirror and sometimes even exceed the size and opulence of the mansions above them. Basement companies refuse to name names, but admit creating mega-basements for top-end bankers, business magnates, footballers and film stars.

Jon Hunt, founder of estate agents Foxtons, applied last year for five floors beneath his house (just across the way from Kensington Palace, Princess Diana's old pad). Plans included a modest underground museum for his collection of vintage cars and motorbikes, and a tennis court. His plans were rejected – more on that later – but there are plenty more being built.

In Chelsea, 23 Cadogan Place (£24m, Savills), has an underground swimming pool, gym, steam room, staff bedroom and cinema. Over in Kensington, 23 Upper Phillimore Gardens (£35m, also Savills) has all those things, plus a wine cellar, large playroom and staff quarters, while 21 Grosvenor Mews in Belgravia has a car lift, garden with sliding roof, and, plunging the entire height of two above-ground and two subterranean floors, a nine-metre interior decorative “waterfall” of water trickling down bronze slabs (bought in December 2009 by a French businessman and his Russian wife for £7.5m, a record for a mews house).

Tom Tangney, partner at estate agents Knight Frank, says: “My favourite basement has a swimming pool with two deep ends so the owner can do tumble-turns. In the arched space beneath, there's a vaulted wine cellar.” Other popular additions include swimming pools with sliding roofs, party rooms and spa facilities.

Derek Taylor, head of development control for the Royal Borough of Kensington and Chelsea, says: “Ten years ago, there were virtually no applications to dig large basements. Four years ago, it seemed that every second application was a basement conversion.” In the past three years, the borough granted 461 “digging-down” applications, rejected 42 and 66 are pending.

The basement boom began, strangely enough, in the genteel upper-middle class west London suburb of Fulham. “It all started in the late 1980s, on Fulham's Peterborough Estate,” says Jeremy Fisher, whose firm Jeremy Fisher Building has been “digging down” since the craze began. “Traditionally, the British middle class didn't spend much on kitting out houses. They'd be content with old central heating and mouldy bathrooms. That all changed in the 1980s. Fulham's residents – mostly City bankers, lawyers and so on – looked to modernise and expand. Houses on Fulham's Peterborough Estate already had large basements, so residents expanded downwards.”