Media playback is unsupported on your device Media caption Brompton Road, which was once a tube station, is now privately-owned

I have been invited on a rather unusual tour of London. It starts very close to the Houses of Parliament but neither Westminster nor Buckingham Palace are on the itinerary.

Instead we are being asked to look out for a different kind of landmark, an apartment that takes up two floors in a grand building near the Ministry of Defence.

As I admire the ornate plasterwork on the balconies of a Victorian mansion block, our guide tells us the apartment belongs to a high-ranking Russian official.

It isn't owned by him directly, but by a company our tour guide claims is connected to him.

It's this lack of transparency that troubles the organisers of today's tour.

"The price of this property is 114 times his annual income," says our guide, Vladimir Ashurkov.

Foreign-owned London Percentage of properties bought through offshore companies 9.3% City of Westminster 7.3% Kensington & Chelsea

4.5% City of London BBC

Mr Ashurkov, a 44-year old former banker and a politician, fled Russia two years ago, and was granted asylum in Britain. He works closely with the Russian opposition leader, Alexei Navalny.

In the central London borough of Westminster, almost one in ten properties is owned by an anonymous offshore company and can't be directly associated with a specific owner, says Transparency International.

In Kensington and Chelsea the figure is 7.3%, and in the City of London the figure is 4.5%. It's claimed that across London there are more than 36,000 such properties.

Image caption All aboard for a coach tour of London's offshore-owned properties

Hidden ownership

But just because the properties are held by anonymous companies does not imply that their purchasers have broken the law - in London it is perfectly legal to buy properties this way.

And that is what the organisers of this tour - ClampK, the Henry Jackson Society, and the Hudson Institute's Kleptocracy Initiative - object to.

They argue it is possible to use ill-gotten funds to buy property without much danger of being asked to account for it; they suggest this makes London property an easy way for wealthy foreigners to "launder" money and evade taxes.

The BBC has no evidence that any of the properties on this tour have been bought either with laundered money or for the purposes of tax evasion. But the organisers argue that the system means it is likely.

Roman Borisovich, 46, another Russian expat and former banker, who has lived in London since 1997, is ClampK's founder.

In a quiet moment he tells me what drew him to London in the first place.

"I adored London for the fact that it was based on the rule of law and for its tolerance of foreigners like me," he says. But now he says he is concerned about "the erosion of this law-based culture".

'Red Square'

The tour takes us to Belgrave Square in central London. It is lined with elegant porticoed 19th Century houses and foreign embassies clustered around a shared garden, a stone's throw from Buckingham Palace.

It has recently acquired a new, unofficial name, "Red Square", thanks to wealthy investors from former Soviet states moving in.

Image caption Many foreign buyers want "property close to the royal family", says Mark Hollingsworth

"Like a lot of foreign billionaires [oligarchs] have this bizarre view that Britain is run by the royal family and the House of Lords," says Mark Hollingsworth, co-author of Londongrad: from Russia with Cash - another of our tour guides.

Having property in central London bestows respectability, says Mr Hollingsworth, and the capital also offers instant access to international banking and legal services.

'Trickledown' effect

Assuming the vast majority of these purchases are legitimate, there is no reason not to welcome the investment, argue many of those involved in London's property market.

"I believe in the economic trickledown effect," says Peter Wetherell, the founder of a highly successful and reputable London estate agent.

"When people buy these expensive properties you have an economic benefit from it - to builders, interior designers, those who fit carpets, kitchens, to employment."

He's showing me around a three-bedroom apartment in Mayfair, with a rather attractive marble-clad bathroom - currently on offer at a reduced price of £6m.

Image caption There is an economic benefit

"When the British had money in the 1960s and 1970s we bought property in Spain, Portugal and Greece, and we spread our wealth around the world," he says.

"Now the world wants to spread its wealth and bring it to London."

But pressure is mounting in the UK to change the current system, and its lack of transparency.

On board the bus with me are representatives from NGOs, writers and politicians from the all-party parliamentary group on anti-corruption, all of whom express concern that the current system could permit money-laundering.

"Three-quarters of properties being purchased are purchased in secret, that's wrong - it ought to be completely transparent," says group member, Labour peer Jeff Rooker.

The government is planning a consultation on the issue later in the year and the first register of all beneficiary owners of all UK companies will be introduced from July.

This will make ownership through UK companies more transparent, but won't affect overseas companies investing in London.

Tighter rules

Our tour culminates at Witanhurst House in the affluent north London suburb of Highgate.

"A palace second in size only to Buckingham Palace, it was sold for £50m to an offshore company registered in the British Virgin Islands," says our guide, and tells us it will soon become home to a Russian oligarch.

I hear the noise of diggers and machinery building a spa and a private underground car park. A neighbour walking the dog nearby mutters how disruptive this has been and how the trees have been cut down.

Image caption Witanhurst House was sold for £50m to a British Virgin Islands registered company

But this kind of disruption could soon be curtailed if increasing clarity on ownership puts off future buyers.

The US, another attractive location for anonymous property purchases, has tightened regulations recently. The US Treasury department announced two months ago that it would start identifying the anonymous buyers of luxury properties, particularly in New York and Miami.

This measure follows the introduction of a strict new anti-money laundering regulations, which have led to the US authorities to impose hefty fines on major banks.

The pressure to shut down avenues of money laundering and tax evasion could also mean property purchases here soon come under tougher scrutiny.

And then our tour guides will be able to pack up and go home.