The hard truth, Tim Farron told the Liberal Democrats in his party conference speech today, is that the NHS needs more money. Actually, that’s a fairly easily stated truth, and widely understood. As Mr Farron made clear, the NHS needs a lot more money – tens of billions of pounds was the Lib Dem leader’s figure. But where is it going to come from?

Political parties rarely lose votes by promising to spend more on the NHS, as the leave campaign so spectacularly – and mendaciously – showed in June. Yet in spite of the public’s love for the NHS, party politicians put their credibility at risk if they cannot say how the necessary cash is going to be raised. This is a problem for all parties in all parts of the UK. The answer is too important be perpetually fudged. The Lib Dems’ latest answer is a cross-party commission modelled, with more than a little touch of hubris, on the Beveridge report, plus a pledge that taxes will rise if the commission’s conclusions require it.

That may seem a cautious approach, but it is hard to think of an issue where getting it right is more important. Every part of the NHS is bursting at the seams. In England, the Conservative election promise of a seven-day service is undeliverable because there is too little money to pay the junior doctors to operate it. This week, NHS England started trying to squeeze more out of consultants for the NHS by publishing details of their private sector earnings. Meanwhile in Scotland, lack of funding may result in a shortfall of 800 family doctors by 2020, according to GPs, while a lack of nurses in Wales is highlighted in a new survey there.

Under David Cameron, the Conservatives just about managed to hold their ground on health by maintaining NHS spending in real terms after 2010 and finding enough extra money in the 2015 autumn statement to get the system through last winter. Theresa May, by contrast, has not yet revealed her hand. Yet a lot of political capital is now being used up in the junior doctors’ dispute and, with hospitals and trusts increasingly sliding into the red, the new chancellor Philip Hammond is under huge pressure to give the NHS a serious boost in this year’s autumn statement, due on 23 November. Whether it will overturn the Tories’ traditionally low trust rating on the NHS is doubtful.

Yet Labour has trust issues too. Health is one of the few policies on which Labour scores better with the public than the Tories. Yet Jeremy Corbyn has focused his leadership campaign on the issue of “renationalisation” of the NHS rather than on saying how he would finance an expanded service. His rival, Owen Smith, has been more precise, pledging 4% extra spending and committing to a wealth tax and a financial transaction tax to help pay for it. It remains far from clear where the party now stands on health spending, other than being in favour of it.

Extra taxes are rarely a vote winner in modern politics. Can hypothecated NHS taxes break the mould? In Scotland, the SNP remains very wary of them, even though under pressure on health. In England and Wales, with the Tories in trouble on the NHS, the more positive opposition arguments that will be needed in 2020 have barely been heard. The Lib Dems are a tiny party now, with only eight MPs. Yet with Labour distracted, Mr Farron’s approach on paying for the NHS may prove in the end to be the most credible of the party conference season.