That Andy Burnham has raised the possibility of tax rises in the autumn Budget is unsurprising. The real question is how he can raise more money without harming the economy. There is a way, but a lot of people won’t like it, because it means taxing houses more.

It’s just an acceptance of the fiscal facts. Britain has a large and unsustainable gap between the money the state raises in tax and the money it spends. That gap is filled by borrowing, which leads to a national debt close to £3trn and an annual interest bill on that debt exceeding £100bn.

Raising taxes is both easy and difficult. Easy because a government has near-complete control of the tax system: if the chancellor wants to increase a tax, he just orders it to rise and Parliament nods through the relevant paperwork. Difficult, because making people or organisations pay more money in tax makes them unhappy.

It also has economic consequences. Generally, raising taxes is bad for growth. Money you pay the government in tax is money you can’t spend on stuff that generates profit for the people making and selling it. It’s also money you can’t invest in stuff that makes your business more efficient.

Rachel Reeves learned this lesson the hard way. Like John Healey, she was fenced in by the Labour manifesto, which rules out increasing the taxes that are the biggest revenue-generators: income tax, VAT and corporation tax.

That’s how she ended up increasing national insurance for employers. It didn’t deliver immediate pain for voters, but it made it more expensive for companies to employ people. Burnham’s tax puzzle then is how to find more money for the state without smothering the UK’s already feeble growth.

Happily, economists have already answered this puzzle, even if politicians would generally rather not admit it. Long-standing research from the OECD, accepted widely across the spectrum, shows that the most growth-friendly way to raise tax is via a recurring tax on immovable property.

That’s largely because property taxes are hard to reduce by changing your behaviour. A house cannot leave the country in response to higher taxes. It cannot lay off staff when its costs rise. You cannot reduce your property tax bill by working less. So if Burnham must raise tax, he should start with houses.

Taxing property more and better would have two strands.

First, revalue and reband council tax in England, which absurdly remains based on 1991 property values – imagine taxing people on how much they were earning 35 years ago. A revenue-raising reform here would add more and higher bands at the top end of the value scale, so the most expensive homes pay something proportionate to their value.

Second, fix stamp duty, which most economists agree is highly inefficient in that it punishes people for moving house. Better to tax the asset rather than the transaction.

This is one of those rare areas where thinkers on the left and right agree. The Labour-aligned Institute for Public Policy Research and Conservative-linked Onward think-tanks have both said stamp duty should be scrapped and replaced with a “proportional property tax”.

Onward suggests a national proportional property tax, levied on house values above £500,000. This rate would be set by central government. The author of that paper, Lib Dem peer Tim Leunig, reckons an annual rate of 0.54 per cent, with a 0.28 per cent supplement on values over £1m, would raise the same amount as stamp duty currently does. Setting the rates above those levels would naturally raise extra money for the Treasury.

With the right set of property tax reforms, it would be technically quite straightforward for a Burnham government to raise between £5bn and £10bn in additional tax revenues and – crucially – do so without harming growth.

All that’s left is the politics, which are, frankly, agonising. People who own homes don’t like the idea of paying more tax on them, and their voices sound loudly in politics and the media. And because of the skewed nature of the UK economy and property market, this tax plan would hit London and the South East hardest.

That might well fit with Burnham’s pledge to rebalance the country away from the capital, but what about his colleagues? Labour currently holds 56 out of 76 seats in London, and 35 more across the South East. Taxing property remains the least bad way to find more money for the public finances, but that doesn’t mean it would be easy for Burnham and Healey.