Rishi Sunak needs a gamechanger to have any hope of leading the Conservatives to victory at the next general election. Sir Keir Starmer could do with something to seal the deal with the British public.

The conventional wisdom is that there are no easy wins available to either the prime minister or the leader of the opposition in these straitened times. But the conventional wisdom is wrong. There is one policy that would be both popular and make economic sense, and that is reform of the UK’s Property taxation.

It is now three decades since John Major’s government replaced the hated poll tax with the Council Tax, a move born out of expediency. That the poll tax was a daft idea was obvious to almost everybody apart from Margaret Thatcher. There were riots on the streets and the unpopularity of the tax was reflected in some thumping byelection defeats for the Tories. In the end, it did for Thatcher.

Abolishing the poll tax left Major with the headache of finding a replacement for it. The answer was Council tax, a system based on a series of bands under which people in cheaper homes paid less than those in more expensive properties. The change was always seen as a short-term fix to give the Tories a chance of winning the 1992 election, which they succeeded in doing. Nobody thought it would still be around today in its original form.

Yet, largely owing to political cowardice the council tax is still with us. The valuations used to calculate bills date back to 1991 even though average prices have risen almost fivefold over that period, and by a lot more than that in property hotspots.

The result of 30 years of inertia has meant the UK has a property tax system that is regressive, inter-generationally unfair and accentuates the North-South divide. According to the lobby group Fairer Share, someone living in a modest £150,000 a year home in Bolton is paying more than £2,700 a year in council tax – £1,000 more than someone occupying an £8m home in London’s Westminster.

Fairer Share proposes replacing council tax – together with stamp duty and the bedroom tax – with a proportional property tax (PPT) based on values uprated annually. The tax would be levied at a flat rate of 0.48%, apart from on second homes and empty homes when it would be 0.96%. At that level, the PPT would raise an extra £5bn a year or so for the Treasury, but if the government wanted to make the new system tax-neutral it could do so by lowering the rates to 0.4% and 0.8% respectively.

Opinion polls suggest that a move to a PPT would be popular, not just because council tax bills have just gone up but because 77% of households would gain from the switch to a different system. There would be an average £556 a year tax cut for 19m low- and middle-income households, while in the 10% most deprived constituencies in England 99% would gain.

Clearly, if there are winners from a PPT then there will also be losers, and these will tend to be concentrated in parts of London and the south-east, where property prices have rocketed since the early 1990s. To avoid making the switch too burdensome, Fairer Share proposes capping the increase under a PPT to £100 a month. The tipping point at which people would start paying more would be about £500,000, which is roughly double the current average house price.

So what’s not to like about a PPT? One argument is that it would be technically difficult to update properties annually. But if Denmark and the Netherlands can manage it, then so can the UK. Anybody who wants to know the current value of their home only has to log on to Zoopla or Rightmove.

Another objection to a PPT is that people who are asset rich but cash poor wouldn’t be able to afford an increase in their bills, even with the increase capped at £100 a month. But people who live in expensive homes on relatively low incomes would have a choice. Either they could downsize to a smaller home on which the PPT would be lower or they could stay put and defer payment until the property was sold.

The real objection to a shake-up of property taxation is political. Although there are supporters of a PPT across the political spectrum (John McDonnell, Vince Cable and David Willetts have all endorsed it), governments have ducked reform because they fear a backlash from those who would lose out, fanned by the rightwing media. Labour had 13 years between 1997 and 2010 and did nothing. The Conservatives have left well alone in the 13 years since.

Polling evidence suggests that concerns about “mansion tax bombshell” are exaggerated. Voters support a PPT by a majority of three to one, with even stronger backing in the Midlands, the North and Scotland. Andrew Dixon, the founder of Fair Share, says that if either Sunak or Starmer put a PPT in their party’s manifesto they would clean up in the “red wall” seats that will help decide who wins the next election.

The arguments against changing Britain’s system of property taxation are weak, especially when set against the obvious benefits. It is not only council tax that is the problem, either. Stamp duty might be a reliable source of revenue for the Treasury but it is bad for the economy because it hinders labour mobility.

This weekend marks the traditional start of the annual housebuying season. With local elections only a month away, there would be no better time that the days of council tax and stamp duty are numbered. Change is long overdue.