Khan has given a £500,000 grant to not-for-profit developers Naked House, who say they were inspired by their own difficulties finding affordable housing.
"Our solution is to strip it back to the bare essentials - saving design and build costs by creating a community of 'naked' houses," they say.
"It's then down to the people who'll live there to create the homes they want. We think this will create homes better suited to people's needs. And we hope the process itself will build a real sense of community."
They say they are hoping to develop another seven sites in the city, and that the model could in theory be rolled out across the UK.
Similar 'shell' homes have been popular in the Netherlands for years. However, they're not being welcomed by all, with Conservative Andrew Boff, who chairs the London Assembly housing committee, saying they don't appear to be designed for families.
"They are for singletons and couples," he tells the Guardian.
"They need homes as well, but if we don't build larger properties for families we are creating a time bomb in London. There are over 300,000 children growing up in overcrowded conditions and that number is rising."
Affordable housing is in short supply all over the country. According to Shelter, typical new homes built today are out of reach for eight in ten working private renting families across the country – even if they use the government's Help to Buy scheme.
"The current way of building homes has had its day and it has failed the nation," says Graeme Brown, Shelter's interim chief executive.
"The only way to fix our ever-growing housing crisis is for the government to champion a bold new approach which responds to communities to build the genuinely affordable, beautiful homes they want."
Least affordable places to live
Least affordable places to live
In Oxford, the average house costs 14.9 times the average salary. With relatively strong local salaries this has much to do with the price of property - at an average of £426,000 (according to Zoopla).
This in turn isn't helped by the fact that the Medieval town and its jam-packed environs do not lend themselves easily to building more property in order to alleviate the problem.
Here the average house is 13.9 times more expensive than the average wage.
Salaries are far higher than elsewhere in the country, but the fact that the average property now costs an astonishing £601,000 (according to Zoopla), makes it the second least affordable place in the country.
The average house now costs 12.7 times the average salary, and Zoopla says the average asking price is now £380,000.
But this picture is getting worse, and may well see Cambridge rise further up the list next year. It is already the fastest-selling location in the UK, so price rises are unlikely to calm down any time soon, and there’s no chance that wages could keep pace.
The average home now costs 10.9 times the average salary, and Zoopla says the average selling price is now a heady £325,000.
Brighton combines a vibrant local cultural scene with handy links to London, so was always going to see demand far exceed the supply of houses. And as London prices have gone through the roof, local prices have followed.
The average property now costs 10.6 times the average salary, and Zoopla calculates that the average selling price is £250,000.
Prices are rising at 5% a year, which means that in most instances wages are failing to keep pace.
An average property price of £276,000 (according to Zoopla) means that they are 10.1 times the average salary.
Prices are also continuing to rise briskly, and are up almost 8% on this time last year, so buyers who waited a year in the hope that houses would become more affordable will be sorely disappointed.
The average property costs 9.5 times the average salary, at £263,000 (according to Zoopla). Prices have been soaring in recent years, and are up more than 10% from this time last year and almost 20% from two years ago.
Average properties are currently 9 times the average salary, at £356,000 (according to Zoopla), but this is set to get worse.
Once Crossrail is finally built in 2019, London commuters are likely to flock in even larger numbers, and prices rise still further.
The average property costs 8.7 times the average salary, at an average of £264,000. Prices are also rising faster than elsewhere in the country and Zoopla calculates they are up more than 10% in a year and almost 15% in two years.
This close neighbour of Brighton has traditionally been seen as its quieter and more affordable sibling, but with average house prices now 8.6 times the average salary, the word ‘affordable’ doesn't really apply any more. Zoopla calculates the average selling price at £272,000.