You know how it is. You've got £30m-£50m to spend on a home and you can't find a thing that's suitable. That's the bizarre situation the world's super wealthy now find themselves in, as a result of the boom in London's super-prime property market.

According to the small but influential group of agents that discreetly buy and sell the capital's priciest properties, desirable homes in the £50m to £200m category are proving as elusive as a Bugatti sports car.

And if you want one where a developer hasn't already marbled the bathroom – one where you can choose where to put the pool or nanny's quarters, or the latest security measures – they are, it seems, proving almost impossible to find in a market that's already risen by 5% this year.

Google chairman Eric Schmidt.

Eric Schmidt, the billionaire chairman of Google, is just one of many trying – and so far failing – to find a suitable home despite his willingness to part with over £30m.

The internet entrepreneur has appointed a friend of Prince William to find him a family-sized home in the upmarket London neighbourhoods of Chelsea or Holland Park. He is yet to find somewhere despite being described as not a particularly "fussy buyer".

The Guardian is aware of at least one famous footballer who is struggling to find a suitable home in central London with a similar sum to Schmidt at his disposal.

David Adams, whose agency John Taylor specialises in marketing luxury homes with an average asking price of £15.5m, said it was getting harder to find homes at the very top of the market that met his clients' exacting needs.

Meanwhile, Noel De Keyzer, who heads the Sloane Street branch of Savills, which sells homes for up to £100m in Belgravia, said the number of properties on his books was half the level of five years ago.

While Rightmove lists properties going for many millions – including one "unmodernised" pad that can be yours for £65m, Adams said most super-prime properties would never appear in an estate agent's window. "Buyers and sellers at the very top of the market are increasingly choosing to do their business away from the public gaze. Around 65% of our business is now conducted off-market."

One issue is security – which is high on any super-prime buyer's shopping list. They want bulletproof garage doors and iris-recognition door key technology – and they don't want the interior, exterior or floorplans of their home in the public domain.

"Buyers don't want homes that have appeared all over the internet for security reasons," says Adams. Another is tax. "If the government were ever stupid enough to introduce a mansion tax, it would be hard for a buyer's lawyer to deny a valuation, if that sum had appeared on the web."

He said vendors who don't want the world to know they are selling up ask him, and a handful of other top agents, to quietly offer their multimillion pound homes to those who have the money

Another high-end property agent, Henry Pryor, described how names of the top agents were usually passed between friends and acquaintances at dinner parties. "It's how the market is right now," he said.

According to investment firm London Central Portfolio, there have only been nine properties sold for more than £20m in London so far this year, although these figures exclude those bought in the name of a company, a technique used by many overseas buyers.

Agents report houses in the £1m-£2m price bracket selling fast, but fear the £6m-£15m market is flooded with sellers who are rushing to cash in on recent prices. De Keyzer said at the very top end, properties were simply not changing hands.

"A lot of the international buyers who bought a few years ago have seen the values of those properties rise – in Knightsbridge, for example prices have gone up by 130% over the last five years. The owners are not in debt, so they don't need to sell," he said.

Earlier this week the Office of National Statistics said property prices in London had risen by almost 10% in the year to July. Land Registry figures have reported that sold prices in Kensington & Chelsea now average more than £1.1m – indeed the space taken up by a doormat in the royal borough is now worth more than £3,500.