There is no shortage of explanations, and no shortage of solutions. But the problem that lies behind our multiple housing crises is simple and obvious. It is, at root, a failure to tax.

Another record tumbled last week. In April, we discovered, house prices in London rose by 4.2%: the largest monthly rate in British history. Young people must mortgage their working lives to service the profits of those who got there first.

As Professor Danny Dorling notes in his book All That Is Solid: “No other city in the developed world contains such a deep – and growing – chasm between rich and poor.” No other city “is surrounded by an entire region where the average house price exceeds £200,000”. Yet our capital contains the largest number of people in poverty of any city in western Europe.

If you buy, you are sucked into a vortex of debt and insecurity. If you don’t, you are forced into a rental market of Dickensian cruelty. Rents in this captive market rose by 9% in London in 2012, while median earnings rose by 2%. Landlords possess the kind of power once wielded by Norman barons. They let out properties that would make great homes for frogs (damp, cold, plenty of insects). If you complain you run the risk of a revenge eviction.

The profits are amazing: an average of 16.3% on a buy-to-let mortgage over the past 18 years. Last year, the Daily Mirror introduced us to a man called Charles Gow. He is the son of Ian Gow, a Conservative housing minister who presided over Margaret Thatcher’s policy of selling council houses to their tenants at massive discounts. Charles Gow now owns with his wife at least 40 former council flats on just one estate in south London. When he started buying, in 1996, they were worth £100,000 each. Now they are valued at £300,000 or more, and he rents them out for £1,500 a month.

You can judge the extent to which ours has become a rentier economy by the furious response to Ed Miliband’s timid proposals to regulate letting. “Venezuelan-style rent controls,” said the Conservative party chairman, Grant Shapps. “The most stupid and counter-productive policy that we have seen from a mainstream party leader for many years,” stomped Stephen Pollard for the Daily Mail.

While Miliband’s proposals would be of some use, they ignore the underlying problem: a consistent failure to tax property progressively and strategically. The United Kingdom is remarkable in that it imposes no land value tax and no capital gains tax on principal residences; and charges council taxes that appear to be the most regressive major levies of any kind anywhere in western Europe. The only capital tax on first homes is stamp duty, but that recoups a tiny proportion of their value when averaged across the years of ownership. Remarkably, it is imposed on the buyer, not the seller.

Why should capital gains tax not apply to first homes, when they are the country’s primary source of unearned income? Why should council tax banding ensure that the owners of cheap houses are charged at a far greater relative rate than the owners of expensive houses? Why should Rinat Akhmetov pay less council tax for his £136m flat in London than the owners of a £200,000 house in Blackburn? Why should second, third and fourth homes not be charged punitive rates of council tax, rather than qualifying, in many boroughs, for discounts?

The answer, of course, is power: the power of those who benefit from the iniquities of our property market. But think of what fairer taxes would deliver.

House prices have risen so much partly because all the increment accrues to the owner. Were the state to harvest a significant part of this unearned income, it would hold prices down and dampen speculative booms. A land value tax would penalise the owners of empty homes: the resulting rise in supply would also help to suppress prices. The money the state recouped could be used to build affordable housing.

Perhaps the most useful tax would be a levy on under-occupancy. In 2011 I proposed a kind of bedroom tax for the private sector: owners with two spare bedrooms or more should be subject to higher property taxes. This was after I stumbled across some buried government figures showing a 45% increase (to nearly 8m) in the number of under-occupied homes in England in just six years. An under-occupancy tax would encourage people either to sell houses that were bigger than they needed to families that could make better use of them, or to divide them, or to take in lodgers.

The howls of execration from the rightwing press still ring in my ears. A columnist in the Telegraph described my idea as “far closer to fascism than the ethno-centric populism of the European radical right”. But when, the following year, the government introduced a bedroom tax aimed not – like mine – at rich owners, but at poor tenants, and with a lower threshold (one spare bedroom, not two), there arose from the same quarters a genteel murmur of approbation.

Now Danny Dorling reveals that “the supply of dwellings and especially rooms per person has never been higher”. What we are faced with, he says, is not a crisis of supply but a crisis of distribution. In England and Wales there are 55 million people and 66m bedrooms: if no one shared a room there would still be more than enough.

Even in London there are more bedrooms than people: a greater supply of housing per head than there has ever been. But because inequality has been expanding even faster than extensions and conversions, most of this abundance of space is in the hands of the people who need it least. A well-aimed tax would help to match housing to need – and would doubtless prompt a major reassessment of how much new building is really required.

When an obvious answer is ignored or repudiated by almost everyone, you see that this is a problem which is not supposed to be solved. The government’s measures – Help to Buy, less planning control, incentives for landlords – are not intended to accommodate those in greatest need. They accommodate the unjust system that keeps them there.

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