Remember that first thrill of a Labour government arriving in office, armed with radical policies that eons of Conservative governments had always labelled impossible?

Jacinda Ardern, New Zealand’s new prime minister, has just announced a ban on selling properties to foreigners. New Zealand has become a safe haven for the world’s hyper-rich, scared that Donald Trump will start Armageddon. Buying a bolthole safe from doomsday has become the fashion in Silicon Valley, as well as among global oligarchs. New Zealand house prices shot up by 10.4% last year.

In Britain the phenomenon of foreigners buying property to mothball as an investment is a London disease, spreading elsewhere. The capital’s latest monstrosity is Versace Tower in Nine Elms, not due to be finished until 2020, but with 170 flats already sold, the top-floor duplex costing £13m. The London Evening Standard, with breathless adulation, describes how everything is Versace-branded, the big V stamped on its gold-filigree chandeliers. Who is buying? Gulf states, Hong Kong, Russia, Iran, Pakistan: “Most of them already have several homes,” says the tower’s agent.

Another hideous blot on the skyline is no more than gold bars in the bank, joining acres of vacant, dead-eyed streets. Kensington and Chelsea – where the Grenfell Tower fire happened – is the only London borough with a shrinking population, due to empty property bought as investment. Land used for luxury emptiness has gone for ever: the London mayor reports 80% of new property built is only affordable to 8% of London’s population. Where are those on ordinary incomes to live?

A Versace-designed dining room in a new Nine Elms tower

Vancouver charges a 1% penalty on homes that are empty for more than six months; councils in Britain should be free to impose any local tax they feel might help their housing market. Labour puts the number of long-term vacant properties at 200,000. The council tax penalty is piffling, but a swingeing tax on vacancies would release a flood of homes for sale or rent, helping to depress prices.

But the only long-term answer to the housing crisis is to build, build, build in places with jobs – yet fewer homes than ever were built last year. George Osborne’s £10bn “help to buy” initiative only inflated prices and enriched builders.

Imagine instead a government arriving in office determined to chill the market and stop house prices rising above inflation. Any rise would be reported as a Treasury target failure – not, as now, another gleeful bonanza for homeowners. Charge capital gains tax on any above-inflation price rise and people would stop regarding their homes as one-way-bet casinos.

The London mayor reports 80% of new property built is affordable only to 8% of London’s population

My generation made a fortune out of unearned windfalls generated by astronomical price rises for properties bought cheap long ago. The social care minister, Jackie Doyle-Price, braved homeowner wrath by suggesting we should use this untaxed housing wealth to pay for our own care in old age, without burdening younger taxpayers. The outcry was instant: she was hammered for denying the right to pass on lavish inheritances.

It would be easy and popular to curb foreign investors and stop insane luxury development on scarce land. But the real housing problem is here at home, among ourselves. We need 250,000 homes a year, every year, never mind the nimbys. Councils need an unrestrained right to borrow to build social housing, with a guarantee that they won’t be forced to sell. The generation that won the property lottery needs to let go of its sense of God-given entitlement.

When Labour comes back in, we need a government that dares to intervene radically in an utterly dysfunctional housing market, defying myriad vested interests – mostly those of existing homeowners.

• Polly Toynbee is a Guardian columnist