One undeniable fact about universal welfare provision is that affluent people benefit. If they break their leg playing polo or, perhaps, overdo it on the Dom Pérignon and need their stomach pumping, a billionaire is as entitled to treatment at the nearest A&E as you are. They can send children to the local school, free of charge (even if most of the very wealthy tend to opt for the private sector). Their parents can claim winter fuel allowance, and many wealthy pensioners do so, not to mention their free bus pass.

Looking at it from one perspective, this makes universality a terrible waste. You’re raising all of that revenue from taxes and then giving some of it back to people who are quite capable of funding whatever it is themselves privately. What if the NHS required everyone earning above a certain figure to pay hotel rates for overnight hospital stays, and asked poorer people to fill in a form to be allowed to stay for free? With the healthcare budget as stretched as it is, the money could be put to all kinds of good use. And shouldn’t higher earners have to contribute a fee if they decide to put their children in state education? Think of the books and equipment it could pay for.

Of course, the relatively affluent already do contribute more towards the cost of public services in the form of taxes (though the very wealthiest have concocted all kinds of schemes to avoid paying what they should). Means testing isn’t necessary to ensure that those who can afford it are asked to pay more. What it represents, in reality, is a rejection of the idea of collectivity. Universal provisions are seen as public goods which benefit the whole of society. Means testing assumes that, ideally speaking, the person making direct use of a service should foot the bill – but help should be provided to those who can’t manage.

The welfare reforms introduced under New Labour were largely means-tested – and so were easy to roll back

Universal aspects of the welfare state tend to be thought of as the fruit of common endeavour. The NHS tops the list of things that make people in this country proud to be British, ahead of the royal family and armed forces. The suggestion that some patients should be charged for hospital visits is likely to make most shudder. Such a reform is widely understood as contrary to everything the NHS is about. Once you’ve introduced a universal provision, it is politically difficult to remove it. Voters are fiercely protective of the entitlements that come to be understood as basic rights.

Means-tested benefits, on the other hand, are seen more as a form of charity. As such, it’s frequently argued that they should go only to the “deserving poor”. The specific definition of “deserving” is a subject of constant public debate. Those further towards the left of the political spectrum are more likely to argue that income level is the only relevant factor. Those on the right tend to see welfare as a tool to control the behaviour of recipients and often insist on additional moral tests. This is the logic that drives the benefit sanctions regime, and the recent cut to child tax credits for families with more than two children.

In recent decades, politicians and certain sections of the press have increasingly pushed the idea that the vast majority of means-tested welfare recipients are “undeserving”. Some amount of fraud is inevitable in any means-tested system, but public perception is that it’s 34 times more common than it actually is.

Stoking resentment in this way has enabled the Conservative government to slash benefits with relatively little backlash. Even people who don’t actively begrudge welfare spending are likely to care less about, say, housing benefit cuts than they do about NHS funding. If you think the economy is like a household budget, means-tested benefits are like charity direct debits. A nice thing to do, but something you can cut back on when times get tough.

When Labour announced, on Wednesday evening, a policy to introduce free school meals for all primary school children, opposition took two main forms. Rightwing commentators decried the plan to fund the programme by introducing VAT on private school fees as an “assault on the well-off” – the same claim they’d make about pretty much any tax rise. Left-leaning critics took a different view. They tended to agree with the tax, but argued universal school meals were not a “progressive” use of the money. That is, it doesn’t redistribute wealth down the income spectrum as efficiently as it might.

It’s true that money spent on middle-class kids’ dinners could theoretically be directed at poorer pupils in more targeted ways, but that misses the point. Maximising cost-effectiveness isn’t what universality is about. Children who receive free school meals report being bullied and stigmatised, and many families who are entitled to claim them avoid doing so for this reason. Others earn just above the £16,190 income threshold but still struggle with the cost of food. Families with an income below the threshold are excluded if a parent works more than 16 hours per week. In some cases, children go hungry not for financial reasons but because of parental neglect. Providing a hot meal to every child ensures that nobody falls through the net.

There’s a solid, practical argument for Labour’s proposal, but focusing only on direct outcomes fails to capture the true challenge facing the party. The welfare reforms introduced under New Labour were largely means-tested. For this reason, the Conservatives have found it easy to roll back much of the progress that was made. The most resilient aspects of our welfare state are the universal provisions which were introduced decades ago.

Mending the welfare state isn’t just about coming up with a spending plan. In 2015, caretaker leader Harriet Harman was so worried about Labour being perceived as the “party of benefits” that she chose not to oppose the principle of a reduction in the household welfare cap – a policy guaranteed to leave families unable to afford their rent. A shift away from means testing and towards universality seems a viable strategy to rebuild a broad base of public support. Theresa May knows that universal programmes are popular, that’s why she’s refused to condemn the free school meals proposal.

Of course the problems with our education system won’t be solved with a single policy, but this could represent a symbolic turning point. Expanding universal provisions could be at the centre of a genuinely exciting vision for the future of the country. More radical options, such as a universal basic income, have also been discussed, but there are all kinds of possibilities. To convince disillusioned voters it has something to offer, Labour needs to be brave and think big. Fiddling with numbers on a spreadsheet won’t cut it.