Chancellor Rishi Sunak is being warned he risks making a “historic mistake” when he unwinds the jobs furlough scheme this weekend amid fresh claims that the UK’s welfare system is ill-prepared for a spike in unemployment.

Keir Starmer and shadow chancellor Anneliese Dodds will say the government has “24 hours to save British jobs” before the Treasury starts cutting back support on Saturday for workers paid to stay at home during the pandemic.

Their plea came as it emerged that a new plan to help the long-term unemployed – trumpeted by Sunak in his Summer Statement – may not be ready until 2021.

The chancellor outlined moves to get what he called “urgent support” to those who would be hit by the new wave of unemployment, doubling the number of work coaches in Job Centres and increasing a support fund.

But HuffPost UK has been told that Sunak’s line that the government was “developing a new scheme to support the long-term unemployed” may not actually materialise this year.

The Department for Work and Pensions (DWP) is still working out the nature of the extra system amid uncertainty over just how many jobs will be lost in coming months.

From this Saturday, employers will have to pay National Insurance and pension contributions for their staff.

And in September, companies will have to pay 10% of furloughed employees’ salaries – rising to 20% in October.

The furlough scheme has supported 9.5 million who have kept 80% of their wages, at a cost of £31.7 billion to date, but ministers say the cost cannot continue indefinitely.

Some employer surveys have shown that nearly half of them are likely to start making people redundant as soon as they are asked to foot the bill themselves for keeping people at home.

Dodds said the move could result in a “python-like” squeeze on jobs in some of the sectors – such as high street retail and hospitality and creative industries – that have been hardest hit by the coronavirus pandemic.

Ahead of a visit to Peterborough, where the party will launch its nationwide jobs campaign on Friday, Dodds said: “The Chancellor’s refusal to abandon his one-size-fits-all withdrawal of furlough is a historic mistake.

“The reward for months of hard work and sacrifice by the British people cannot be a P45. It’s not too late for the Chancellor to see sense, change course and support the businesses and sectors that need it most.”

Labour wants the furlough scheme to be reformed rather than wound down completely, with a focus on key sectors. It is calling for a £1.7 billion “fightback fund” to prevent firms going under and additional support to areas forced into local lockdowns.

SNP Treasury spokeswoman Alison Thewliss also warned that changes to the furlough scheme are “dangerously premature”.

A Government source said that the furlough support had been “comprehensive and generous” and hit back at Labour’s claims.

“The furlough scheme is unprecedented and has so far supported the wages of 9.5 million people, at a cost of £31.7 billion and will run for eight months in total,” they said

“It is not a ‘one-size-fits-all’ policy, it is the most comprehensive and generous version of support that can be provided. The Labour party seem to be very good at calling for things, but repeatedly fail to put forward any realistic or detailed plan on how they can be delivered.

“We are yet to hear for example who they think should be left out of this ‘targeted support’ and why. As the economy reopens, we are adjusting the support provided to ensure people can get back to work and we can rebuild our economy.”

Unison general secretary Dave Prentis said: “The government must pull back from the brink and continue giving a helping hand. People’s livelihoods depend on it.”

Unite boss Len McCluskey added: “If we are to avert the jobs’ loss tsunami that we fear will sweep through our communities this summer, we need the government to act and to do so urgently.”

The DWP, as well as the Treasury, has been praised by the prime minister for the rapid way in which it provided extra support to those forced onto Universal Credit as a way of making up for income lost during the crisis.

But Sunak’s reference to the development of a “new scheme” for the long-term unemployed – classed as those out of work for more than a year – has not yet been backed up with any detail.

It is unclear whether existing schemes will be tweaked or whether a brand new support programme will be rolled out, but no time frame has yet been set for whichever route is chosen.

A spokesperson for the DWP said: “Our Plan for Jobs will create, support and protect jobs, and our immediate focus is on supporting people back into work quickly which is why we’re getting 4,500 new Work Coaches in place for this autumn.

“Meanwhile, officials are working round the clock to get new support for the long term unemployed in place and we will announce further detail including its start date in due course.”

Many of the public are for the first time encountering the Tories’ flagship welfare system, which unifies six different benefits into one payment.

Critics have claimed its level is set too low and that it only offers loans not grants to those in most urgent need.

A cross-party parliamentary report into Universal Credit published on Friday was also highly critical, claiming the system was “failing millions of people”.

“The temporary increase in the standard allowance in response to the Covid-19 pandemic shows that the previous level of awards was too low. The increase should be made permanent,” the Lords economic affairs committee concluded.

The committee said the “punitive nature” of UC “punishes the poorest by taking away their sole source of income for minor infractions” and needs rebalancing.

Committee chairman Tory peer Lord Forsyth of Drumlean said the committee agreed with aim of UC, but its implementation needed change.

“In its current form it fails to provide a dependable safety net. It has led to an unprecedented number of people relying on foodbanks and not being able to pay their rent.”

But Minister for Welfare Delivery Will Quince MP said: “The case for Universal Credit has never been stronger.

“The system defied its critics in unprecedented and unforeseeable circumstances, processing more than 3.2m new claims at pace since mid-March and paying more than a million advances worth hundreds of millions of pounds to those in urgent need within days.

 “We remain committed to supporting the most vulnerable in society, which is why we currently spend over £95 billion a year on the benefits system. We’ve also increased the Universal Credit standard allowance by up to £1,040 a year, as part of a package of welfare measures worth over £9.3 billion.”