There are two housing crises in Britain. One of them is obvious and familiar: the walloping shortfall in supply. Households are forming at roughly twice the rate at which new homes are being built. In England alone, 650,000 homes are classed as overcrowded. Many other people are desperate to move into their own places, but find themselves stuck. Yet the new homes the government says we need – 5.8m by 2033 – threaten to mash our landscapes and overload the environment.

The other crisis is scarcely mentioned. I stumbled across it while researching last week's column, buried on page 33 of a government document about another issue. It's growing even faster than the first crisis – at a rate that's hard to comprehend. Yet you'll seldom hear a squeak about it in the press, in parliament, in government departments or even in the voluntary sector. Given its political sensitivity, perhaps that's not surprising.

The issue is surplus housing – the remarkable growth of space that people don't need. Between 2003 and 2008 (the latest available figures), there was a 45% increase in the number of under-occupied homes in England. The definition of under-occupied varies, but it usually means that households have at least two bedrooms more than they require. This category now accounts for over half the homes in which single people live, and almost a quarter of those used by larger households. Nearly 8m homes – 37% of the total housing stock – are officially under-occupied.

The only occasions on which you'll hear politicians talk about this is when they're referring to public housing. Many local authorities are trying to encourage their tenants to move into smaller homes. But public and social housing account for only 11% of the problem. The government reports that the rise in under-occupation "is entirely due to a large increase within the owner-occupied sector". Nearly half of England's private homeowners are now knocking around in more space than they need.

Why is this happening? I've spent the past few days wading through official figures to try to find out. None of the most obvious explanations appear to fit.

Though the proportion of homes occupied by just one person rose sharply between 1961 and 2001, there has been no increase since then. The formation of single households can't account for the growth in under-occupancy between 2003 and 2008. The proportion of couples without children has also remained stable since 2001. Fertility rates have increased over this period – from 1.63 babies per woman in 2001 to 1.96 in 2009 – so a general absence of children doesn't explain it either. Nor can it be blamed on the elderly: except through devastating war, no population can age by 45% in six years. The divorce rate fell in 2008 to its lowest level since 1979. Marriage has declined, but cohabitation has risen. The overall rate of household formation rose only slightly during the period in which under-occupancy has boomed.

This appears to leave just one likely explanation: money. My guess, though I can find no research or figures either to support or disprove it, is that the richest third of the population has discovered that it can spread its wings. A report by the International Longevity Centre comes to the same conclusion: "Wealth … is the key factor in whether or not we choose to occupy more housing space than is essential."

While most houses are privately owned, the total housing stock is a common resource. Either we ensure that it is used wisely and fairly, or we allow its distribution to become the starkest expression of inequality. The UK appears to have chosen the second option. We have allowed the market, and the market alone, to decide who gets what – which means that families in desperate need of bigger homes are crammed together in squalid conditions, while those who have more space than they know what to do with face neither economic nor social pressure to downsize.

The only answer anyone is prepared to mention is more building: let the rich occupy as much space they wish, and solve the problem by dumping it on the environment, which means – of course – on everyone. I think there's a better way.

While reducing under-occupancy can't solve the crisis of provision by itself, and there will still be a need for new construction, a better distribution of the housing we've built already would help to relieve the pressure on both people and places. First, we need to see the problem. I suggest a new concept: housing footprints. Your housing footprint is the number of bedrooms divided by the number of people in the household. Like ecological footprints, it reminds us that the resource is finite, and that, if some people take more than they need, others are left with less than they need.

The next step is to reverse the UK's daft fiscal incentive to under-occupy your home. If you live by yourself, regardless of the size of your property, you get a 25% council tax discount. The rest of us, in other words, subsidise wealthy single people who want to keep their spare rooms empty. Those who use more than their fair share should pay for the privilege, with a big tax penalty for under-occupation. If it prompts them either to take in a lodger or to move into a smaller home in a lower tax band, so much the better.

I would also like to see an expansion of the Homeshare scheme, which could address several growing problems at once. Instead of paying rent, lodgers – who are vetted and checked by the charity that runs the project – help elderly homeowners with shopping, cleaning, cooking, gardening or driving. Typically they agree to spend 10 hours a week helping out, and to sleep in the house for at least six nights out of seven. This helps older people to stay in their own homes and lead an independent life, gives them companionship and security and relieves some of the pressure on social services and carers. It provides homes for people who wouldn't otherwise be able to afford them.

But we can't solve this problem unless we start to discuss it. It needs to be researched, debated, fought over. It needs to turn political. I can understand why neither the government nor the opposition dares to think about it: none of the major parties wants to pick a fight with wealthy householders. So it's up to us to give them no choice, by turning under-occupation into an issue they can't avoid. It cannot be left to the market, as the market works for the rich.

• A fully referenced version of this article can be found on George Monbiot's website

• The standfirst of this article was amended at 10.10am on 4 January