Rachel Reeves is in favour of radical tax reform – or at least she was in 2018. “We need a radical overhaul of the tax system because our current system of wealth taxation isn’t working,” she argued in her pamphlet The Everyday Economy.

Seven years later, in her second year as chancellor, Reeves appears to be returning to some of the themes in that pamphlet, especially as it relates to the UK’s convoluted and unpopular system of taxing property.

The Guardian revealed on Monday the chancellor was considering scrapping stamp duty (used in England and Northern Ireland) and replacing it with an annual levy based on the value of someone’s home and the time they bought it. On Tuesday, the Times reported that Reeves was also considering imposing the UK-wide capital gains tax on higher-value primary properties, even though the prime minister, Keir Starmer, ruled out doing so before the election.

All this is part of what officials say is a wider examination of the UK’s property tax system, which experts argue could be simplified and improved while also raising money to help fill Reeves’ £20bn fiscal black hole.

“Reeves is so desperate to find money she is flying every kite going [floating policy suggestions] to see which ones get knocked down,” said Tim Leunig, an economist whose work Treasury officials have been studying. “But there are important reasons to change the way our property taxes work, especially if you want to raise serious money.”

Politicians have long looked at inflated property prices in parts of the UK and wondered how to squeeze more money from them.

Vince Cable, the Liberal Democrat former business secretary, proposed a mansion tax in 2009 that would have taxed properties worth more than £1m at 0.5%. The plan was dropped when his party entered government and faced opposition from their Conservative coalition partners.

The idea was taken up by the then Labour leader Ed Miliband, who claimed in the 2015 election campaign that the policy would raise £1.2bn a year.

Until recently, Treasury officials have scoffed at the idea of anything resembling a mansion tax, saying it would encourage wealthy people to move abroad. But they admit the UK’s property taxation system is riddled with problems.

An obvious one is stamp duty, which is a one-off lump sum charged to people when they buy a new property, set at different rates according to the value of the property up to a maximum of 12% for properties worth more than £1.5m.

The problem with such a charge is that it disincentivises property purchases, slowing the economy, and reducing the turnover of new properties. Leunig has suggested instead that property owners pay a smaller annual amount based on the purchase price of the home, payable in perpetuity.

A rate of 0.54% with an additional supplement for properties worth more than £1m would raise the same amount as stamp duty does. A higher rate, or temptingly for the chancellor, a bigger supplement, could raise far more.

Such a system would help those who move frequently, but penalise those who stay in their homes for a long time. Leunig argues this would incentivise people to move into smaller, cheaper properties towards the end of their lives, freeing up larger stock for younger families.

Another problem which many have identified is with council tax, which is both unpopular and messy, with rates based on property valuations from 1991.

Successive government have shied away from a full revaluation, which would create millions of losers, but Leunig has suggested levying a new charge only on properties worth less than £500,000 – with those over that threshold being covered by the replacement for stamp duty.

While officials are looking into potential changes to council tax, this is likely only to come in if Labour wins a second term in office. Ministers are aware that polls suggest raising council tax would be one of the most controversial options they have.

A third problem comes with capital gains tax, which is charged at a rate far below income tax. Officials are now looking at whether to levy CGT on primary properties for the first time, albeit only over a particular threshold.

There are two problems with doing this, however. One is that Starmer explicitly promised not to before the election. And the other is that it would prove a major disincentive for people to move out of larger properties.

“No other countries does this without some form of exemption or rollover which allows sellers to pay it much later down the line,” said Ben Hopkinson, the head of housing at the Centre for Policy Studies.

There is one further problem for the chancellor: British property is already more heavily taxed than that in most other countries. According to the OECD, the UK takes in more property tax as a share of its gross domestic product than any other developed economy.

“Property is inherently difficult to tax,” said Leunig. “But we still manage to do so – at a rate three times higher than Germany.”