Theresa May’s cabinet has agreed a post-Brexit immigration system that will offer visas to immigrants in a tiered system based on skills and wealth, a flagship policy that is expected to be one of her key announcements to the Conservative party conference next week.

Downing Street hopes the migration policy will appeal to party members concerned about May’s leadership and the Brexit negotiations, which last week appeared to have reached an impasse at Salzburg when EU leaders declared her Chequers proposals would not work.

Ministers signed off a plan presented by the home secretary, Sajid Javid, in which skilled workers will more easily be able to obtain visas than the unskilled and in which there will be no preferential access to the UK labour market for EU citizens.

Territories which strike a free trade deal with the UK, including the EU, will be given enhanced access to the British labour market, but that in the future could include the United States, Canada, or elsewhere.

At the same time, no significant concerns were raised by cabinet members about the status of the divorce talks, even though hard Brexiters on the right of her party continued to press for May to change her policy, publishing their alternative “Canada-style” free trade proposal.

Sajid Javid’s immigration proposal exposes the insanity of Brexit | Simon Jenkins Read more

The Brexit negotiations update was held at the end of the cabinet meeting on Monday afternoon and the only person who referred to a Canada-style trade deal was the prime minister herself in her own presentation. She added that some EU heads of government were being more constructive than others behind the scenes, but did not specify which leaders.

The meeting amounted to a moment of relief for the under-pressure prime minister, who heads to New York on Tuesday for a United Nations meeting before turning her attention to the party conference. One cabinet source said May was “just trying to get through the conference season intact”.

A white paper setting out the new immigration policy is due to be published later this autumn.

Last week, the government’s Migration Advisory Committee, a group of independent experts, proposed that the UK implement policy that favoured skilled workers in a paper that paved the way for Javid and May. But its proposal that there should be no visas made available for unskilled workers outside agriculture provoked alarm among business leaders, who said they needed access to a large labour pool to fill jobs in sectors such as construction, haulage and hospitality.

However, a Whitehall source said: “Whilst the MAC report said that low-skilled immigration doesn’t really add anything to the economy, Sajid recognises that for certain types of businesses, including hospitality and social care, you do need that labour flow coming in.

“So it’s about necessity and what the economy requires, but with an absolute guarantee of ending freedom of movement and not having the preferential system.”

There was a “tiny bit of grumbling” from Philip Hammond about potentially extending freedom of movement beyond the transition period but that was “quickly seen off”, sources said.

The chancellor and business secretary Greg Clark both called for more flexibility so businesses could continue to operate. Hammond told colleagues “we need more than just a trade deal” while Clark said “mobility is to services what customs is to trade”, sources revealed. Both men backed the home secretary’s plan.

The welfare secretary, Esther McVey, had what one colleague described as an “indirect pop” at the chancellor. She said: “On the one hand, we’re told that when we leave the EU we will go into a recession. On the other, we’re going to need mass migration. They can’t both be correct.”

Dominic Raab, the Brexit secretary, said after the meeting that ministers had a “good, healthy discussion” and said that the prime minister told those present that “we are going to keep our calm, hold our nerve”.

Government sources also dismissed suggestions that Javid wanted EU citizens to be allowed through the border for a transition period of 30 months if Britain left without a deal. They said that the proposal was one of several raised at a cabinet sub-committee a while ago but no agreement had been reached, and that the 30-month figure has been revised downwards since then.

Ministers are waiting for the EU to come back with its detailed counter-proposals to the Chequers plan in mid-October before deciding what do to next, despite an energetic “chuck Chequers” campaign being fronted by Boris Johnson, David Davis and Jacob-Rees Mogg.

The trio tried to step up the pressure on May ahead of conference following the publication of a report by the rightwing Institute of Economic Affairs thinktank that proposed a deregulated, free-trade future for the UK.

Rees-Mogg told May that she needs to recognise that Chequers does not have much support and that she should think carefully about switching tack to propose that the UK strikes a Canada-style free trade agreement with the EU after Brexit.

The chairman of the hard Brexit-backing European Research Group described May as “a lady of singular wisdom” who was “likely to recognise the reality that Chequers doesn’t have much support” and that “with her wisdom and insight she’ll think carefully about adopting it”.

The MP was speaking an an event attended by a string of critics of May’s Chequers plan, including former Brexit secretary Davis. The group claims the plan would leave the UK forced to share regulations for food and goods with the EU after Brexit.

Rees-Mogg said he believed that because the EU had “snubbed the prime minister” by appearing to reject Chequers at the Salzburg summit last week, the only options were a no-deal Brexit or to propose a last-minute free-trade agreement. He argued that it would be popular with the British public, and said “if we go to the House of Commons it would be passed”.

But at a morning press briefing held at the same time as the IEA event, Downing Street dismissed the idea that a Canada-type free trade agreement could work. Shanker Singham, director of the international trade and competition unit at the IEA, called on ministers to rethink their Brexit strategy. Singham, speaking at the launch of the alternative Brexit plan, said the government’s white paper would “absolutely preclude” a free-trade agreement with the US.

Singham’s report argues that the UK should try to deregulate in comparison to the EU. He said: “Membership of the European Union stifles prosperity just as it prevents the UK governing itself. It saddles the UK with regulations that protect large incumbent businesses from competition, harming innovation and reducing efficiency.”

Davis said the UK’s negotiations with the EU had reached a “cul de sac”. He said that the EU’s rejection of Chequers at Salzburg was “all too predictable” and it would have happened either there or at the European summit due next month.

Boris Johnson did not attend the IEA event, but was quick to praise the report entitled Plan A+ on social media. He tweeted: