What would William Beveridge do? Marking the 75th anniversary of his groundbreaking report, the London School of Economics is asking that question with events on the future of the welfare state: Beveridge was LSE director for almost 20 years. Last week a whole day was devoted to basic income – a universal wage paid regardless of need: an idea, many keep saying, whose time has come. But Beveridge would have been appalled. And so would most voters in their current state of mind. His 1942 cradle-to-grave social insurance plan sprang from a wartime collective spirit, seeming to square an age-old problem. His universal safety net was a great leap forward – though never quite what it claimed to be: there are no silver bullets.

From Tudor poor laws to Victorian workhouses to universal credit, the same political dilemmas face all welfare policies: how to prevent starvation without the moral hazard of encouraging dependence. Beveridge was wary of the predicament. His plans meant you pay in when in work, draw out when in need, earning rights through contributions. This moral basis was instantly politically attractive.

It never worked like that and never could. Housing benefit was left out: it defeats every system. From the start too many couldn’t pay in – those not in work or mothers – yet still needed means-tested national assistance, while older people drew pensions from day one. All governments cling to vestiges of national insurance, by now mostly a sham, because residual belief in it makes it a more acceptable tax. Politicians strive to reinvent social insurance to rekindle faith in benefits, but they always stumble on the same Beveridgean dilemmas: complex lives don’t fit neat solutions.

This Tory era has justified unthinkably savage benefit cuts by undermining public trust

Benefit systems spring from the heart of any nation’s values. That’s why relatively small sums paid to working-age people in need are always fraught and often punitive. Everyone wants “fairness”, but what kind? Iain Duncan Smith (father of four) found it unfair for low-paid families to have too many children so he allowed benefits for just two. But it’s unfair for a child to grow up poor because they have more siblings – or because their parents are low-paid, mentally ill, inept or plain unlucky. Every child deserves an equal chance, say all parties, though rightwingers put punishing the sins of parents ahead of the rights of the child. National identity is wrapped up in these choices, veering between generosity and severity.

Dividing deserving from undeserving, this government is the first to cast disabled people as undeserving, with Tory press releases from the Department for Work and Pensions spreading anecdotes about people running marathons while claiming for disability. This Tory era has justified unthinkably savage benefit cuts by undermining public trust: one shocking story is worth a hundred articles that show fraud accounts for 1.1 % of the benefit bill, little more than sums underclaimed. Arousing taxpayer fears of being cheated is a good cover for sending child poverty soaring to more than 31%, as predicted by the Institute for Fiscal Studies.

Amid this bleakness, the idea of a basic income drops out of the clouds as a refreshing spirit of kindness. Give everyone, rich and poor, enough to live on and at a stroke remove the perverse incentives of means-testing, where people lose 63p in every pound they earn in work. Easy to administer, it encourages work, redistributes wealth and removes penury. Small pilots around the world explore the idea, with Barack Obama and John McDonnell expressing interest.

But it doesn’t square the circle. A full system paying everyone enough to stop means-testing needs a politically impossible tax rise, without extinguishing poverty. A partial system, as the LSE’s Dr Malcolm Torry advocates, seems the worst of both worlds, paying £60 to all but still needing means-testing for low-paid people, and it omits housing benefit. The University of Bath, modelling various levels of taxation, shows that full funding would take abolishing tax allowances and NI limits while raising income tax by between 4% and 8%. The Adam Smith Institute finds “fairness” in basic income as it flattens benefits for the poor, matching their flat taxes for the rich.

The age-old dilemma is how to persuade voters to pay up for redistribution. Not by arousing moral outrage at a very expensive something-for-nothing for all. Basic income idealism distracts from finding better answers. Here’s the clincher: should a chancellor daring to raise high taxes spend it on handouts to the comfortable or target it on the neediest and our threadbare public services?

Torry is a vicar and here is the best of Christian impossibilism. As a thought experiment for countering the monstrosities of our present sanctions-heavy system, basic income is well worth debating. Some think a catastrophic loss of jobs to robots will make this necessary, if a few robot-owners take all the wealth: frankly, in such a dystopia, expect rebellion not orderly wealth transfer.

There are never easy answers: we get the welfare state we pay for. Hypothecate all NHS costs into a replacement for NI? That, too, would soon become bogus, and removing the most popular item from income tax might erode willingness to pay it. Land value tax? Yes, but that’s just one mechanism already abused by the Mail as a “garden tax”: the key issue is how to tax property wealth. Make the old pay fairly for social care? The 2010 Labour manifesto’s good plan for a lump sum paid on retirement was blasted away as a “death tax”. The Tory 2017 manifesto plan was dubbed a “dementia tax”. The great question is how to persuade a tax-phobic country that we pay too little, especially on wealth. But to raise enough for basic income, to borrow Bertolt Brecht’s irony, you need to elect a new set of people as taxpayers first.

Ipsos Mori and the British Social Attitudes survey detect a softening of mood, a pendulum swinging back. Rough sleepers in freezing streets are visible reminders to restore revulsion and shame. A modern Beveridge would seize the moment, while ever cautious about moral hazards. How? Do as Labour did and focus funds on self-evidently blameless children first, their benefits and their Sure Start centres, as the best investment for future national wellbeing.

• Polly Toynbee is a Guardian columnist