This week the Tories unveiled a poster warning of a Labour “tax bombshell”, alleging that Jeremy Corbyn would deprive the army of munitions. But there’s irony there; thanks to their own cuts to defence spending, British warships will have to sail without anti-ship missiles from 2018. Frigates without missiles, hospitals without doctors: that’s what happens if you try to shrink the state but end up suppressing economic growth instead.

Analysis from the Institute for Fiscal Studies shows that the share of national income we spend on schools, defence and policing has fallen significantly since the financial crisis in 2007-08. Services are at breaking point, and households are borrowing hand over fist to pay for childcare, rent and elderly care. Labour can win this election with big, eye-catching pledges that put money back into schools, hospitals and the pockets of hard-pressed families. To do that, it needs a tax bombshell it is prepared to drop. Labour has already promised to borrow £350bn for investment over 10 years, but the money to save the NHS and schools has to come from new taxes.

Where will the money come from? Shadow chancellor John McDonnell has indicated that Labour won’t make any VAT increases, and also looks set to rule out any rises in national insurance. So the money has to come from the wealth of the rich, the profits of big corporations, and from ending the culture of tax avoidance and evasion that pervades Britain, from the Mayfair mansion to the construction site.

If Labour sticks to raising conventional taxes, this will create only a limited pool of extra money for public services – as these taxes barely touch the vast reservoirs of wealth that sit outside company profits and declared personal incomes. So a Labour government would soon push to the limits of what’s achievable through the big three: VAT, corporation tax and income tax. For instance, reversing George Osborne’s corporation tax cut, Labour’s biggest conventional tax pledge to date, would raise £12bn a year. The problem is not, as the Conservatives allege, that this has been spent several times over: it has not. The problem is it’s still only £12bn. So Labour must take the plunge recommended by French economist Thomas Piketty, and increase taxes on wealth.

Wealth slips across borders and is hard to tax, says the conventional wisdom. Well, stand in central London and look upwards. Wealth is indeed slipping across borders – in the form of massive speculative property investments in Britain’s cities. It does not matter how opaque the trusts, or how complex the tax wrappers. The actual glass, steel and concrete reside in the United Kingdom, and should form the centrepiece of a windfall tax of foreign property tycoons. The billions raised would still probably be in single figures, but there’s lots more you can do once you establish the principle that to pay for a modern state you have to tax wealth in its modern form.

Windfall taxes on bank profits and on bankers’ bonuses, and a crackdown on offshore tax avoidance could – if Labour is prepared to be aggressive enough – collect serious amounts of money. So could a financial transaction tax. Touted for more than 20 years by economists on the centre left, the sums raised by a so-called Tobin tax may not be spectacular, because many of its benefits come in the form of financial markets reducing risk and suppressing speculation, thereby lowering any potential tax take.

But in February, former JP Morgan economist Avinash Persaud proposed a plan to extend the UK’s existing tax on share-dealing to bonds and derivatives. Even this modest proposal would generate £5bn a year. In the form advocated by the Trades Union Congress, it could raise at least £20bn.

Whatever Labour does through wealth tax, it is going to have to bite the bullet and restore the 50p tax rate for high earners, even if it doesn’t raise huge amounts. Taxing the top 1% should be a defining principle for a radical social democracy. Corbyn’s Labour should say to those on six-figure salaries that, by paying a bit more, they are getting the cheapest health insurance money can buy, world-class services, a more socially cohesive society – and a navy with actual missiles.

This is the prize. Five billion here, two there, adds up to a war chest that Labour has to be prepared to use as symbolically and politically as the Tories use tax cuts. I am frustrated not by Labour’s tendency to “double spend” its expected receipts – which is a Tory myth easily disproved with a spreadsheet. I am frustrated by the number of rows on that spreadsheet: Labour’s tendency to scatter commitments among worthy causes instead of concentrating them on the principle that matters.

That principle is that a state committed to social justice should provide high-quality universal services: a guaranteed state pension; an unsurpassed health service; free childcare and elderly care for all; and yes, a beefed-up policing, defence and security apparatus to meet rising global threats. And then it should make the case for a redistributive tax system to pay for them.

To an electorate increasingly reconciled to the destruction and privatisation of these universal public goods, a Labour manifesto committed to massive extra spending on services would change the debate. It would be attacked on credibility grounds, as the broadcasters dutifully repeat the objections of rightwing thinktanks that these taxes are uncollectable, or would suppress growth, or lead to capital flight. But a left-led Labour party could ensure it had more than Ed Miliband’s stone slab carved with vague intentions: a spreadsheet backed by professional economists prepared to call out the quack-medicine peddlers and defenders of unearned wealth.

To work, a Labour tax and spend plan must hit only the rich, and benefit everyone – not just the poor. To keep Britain’s economy geared to the needs of foreign oligarchs, tax dodgers and the global banks, Theresa May is prepared to risk both our domestic economy and our national security. Labour should offer a radical alternative.

It may fail. But it has failed in the past through timidity and incompetence. If it fails while armed with a radical programme, at least we know what the electorate has chosen: a navy without missiles, hospitals without doctors, workplaces without rights, exports without a market; a country without hope.