Philip Hammond has told business leaders they need to accept the result of Britain’s EU referendum and warned that a failure to implement it would damage the country’s political stability.

The chancellor told increasingly restless business leaders that he was working for a deal that safeguarded the economy, and said he understood their frustration but companies had to accept that changes were coming – such as an end to the free movement of people and business models built on a supply of cheap labour.

“We need to get the politics right,” Hammond said at a Confederation of British Industry (CBI) lunch in Davos. “Even from the narrowest interpretation of business interests, it would be a pyrrhic victory to meet the needs of the economy, but by shattering the broad economic consensus behind our country’s political and economic system.”

Hammond said a promise had been made to voters in 2016 that they were choosing a more prosperous future. “Not leaving would be a betrayal, but leaving without a deal would also be a betrayal.”

The chancellor is one of several senior members of Theresa May’s government who have become increasingly concerned about the risks of a no-deal Brexit.

The business minister Richard Harrington said on Thursday that he was even prepared to be sacked, after welcoming comments from the Airbus chief executive criticising the government’s handling of Brexit.

“I was delighted to read Airbus’s comments this morning because it is telling it like it is,” Harrington said, adding that a no-deal Brexit would be “a total disaster for the economy”.

Meanwhile, the work and pensions secretary, Amber Rudd, renewed her demand for Conservative MPs to be given a free vote on Tuesday – when MPs will consider amendments to the government’s Brexit motion – so that she could back an extension to article 50.

Rudd said that over the next few days she was “going to stick to trying to persuade the government to allow it to be a free vote. There is a lot taking place and there are a lot of new amendments. We’ll have to wait and see.”

After last week’s crushing parliamentary defeat for May’s Brexit plan, Hammond and the business secretary, Greg Clark, had reassured business leaders that Britain would not leave the EU on 29 March with no deal.

But the chancellor said businesses had to accept that free movement was coming to an end and urged companies to rethink business models based on cheap, low-skilled labour.

The CBI and other employer organisations have expressed concern at some of the proposals contained in the government’s immigration white paper, particularly the idea of strict curbs on entry for people in jobs paying less than £30,000 a year.

Hammond urged the business leaders to engage with the government’s consultation on the white paper, hinting that ministers were open to reducing the £30,000 cap. “Free movement is ending. The detail of what is to replace it has yet to be decided. Business has to seize the opportunity to engage with the process and come up with constructive, consistent and evidence-based solutions.”

The chancellor said businesses had to come up with creative ways of ensuring they had access to people with intermediate skills but would also have to help change Britain’s economic model so it was less dependent on cheap labour.

He said the economy was in good shape, pointing to record employment and growth forecasts that were “perfectly respectable” provided there was an EU deal.

“The only credible and sustainable solution is to leave the EU, to honour the referendum decision, but to do so in a way that allows us to deliver the future prosperity voters were promised when they voted to leave the EU. The only way forward is a negotiated settlement,” he said.

Asked about the comments of Harrington and the chancellor, May’s spokeswoman said the cabinet was “working very closely with the PM on delivering a deal which works for the British economy and for employees”.

Mark Carney, governor of the Bank of England, told a separate Davos event that business was not ready for a no-deal Brexit. “There are a series of logistical issues that need to be solved and it’s quite transparent that in many cases they’re not,” he said.

Border infrastructure was not ready for the possibility of “jumping from an absolutely seamless trading environment to one with frictions that aren’t just tariffs but are rules of origin on products, safety standards on products and other actions that need to be done”, he said.

Referring to cross-border supply chains and the companies that rely on parts reaching them just in time for production, Carney stressed that “minutes matter in this world”.

Business leaders meeting in Davos have said they were implementing no-deal Brexit plans, but Carney said: “There is a limited amount that many businesses can do to prepare if there are going to be substantial delays on the logistical side. These eventually will be worked out over time, but you can’t build up the inventories.”

Meanwhile, union leaders who met with May were critical of her stance. The TUC general secretary, Frances O’Grady, said she had not received the guarantees she was seeking that there would not be a no-deal Brexit, and added: “I was looking for guarantees on workers’ rights now and into the future.

“We have a prime minister on a temporary contract. She cannot bind the hands of a future prime minister.”

Tim Roache, general secretary of the GMB union, said: “I’m afraid to say the prime minister failed to give us the guarantees we need over protecting jobs and rights at work.

“As this crisis worsens, pretending nothing has changed is simply not good enough.”