Rishi Sunak has laid down a red line for any new attempts to improve post-Brexit trade with the EU and managed to quell a rebellion among furious Tories – but kept open the possibility of closer ties with Brussels. The prime minister dismissed suggestions the UK could pursue a Swiss-style relationship with the bloc, while a senior business leader called the row a “sideshow” and No 10 sources pointed the finger of blame at the chancellor, Jeremy Hunt. Addressing the clamour for the first time, Sunak stressed his pro-Brexit credentials as someone who supported leave in the 2016 referendum, and talked up the need to unleash the “enormous benefits and opportunities” of being outside the EU. “Under my leadership, the UK will not assume any relationship with Europe that relies on alignment with EU law,” he pledged at a speech to the Confederation of British Industry (CBI) in Birmingham on Monday. Sunak said that having “regulatory freedom” to diverge on EU standards was a key advantage and insisted it would not be sacrificed in any future talks to try to break down trade barriers with Brussels. He did not dispute suggestions made previously by Hunt that the UK should “remove the vast majority of the trade barriers that exist between us and the EU” while remaining outside the single market. No 10 later said the pair were “absolutely” in agreement on Brexit policy, and confirmed that ending freedom of movement and “unnecessary payments” to the EU, as well as retaining the UK’s ability to strike trade deals, were also red lines. Keir Starmer, the Labour leader, is to tell business leaders the days of “low pay and cheap labour” must end in his own address to the CBI on Tuesday. He is expected to vow to be “pragmatic” about the shortage of workers and not ignore the need for skilled migrants, but stress that any changes to the points-based migration system “will come with new conditions for business”. “We will expect you to bring forward a clear plan for higher skills and more training, for better pay and conditions, for investment in new technology,” Starmer will say. In a sign of Sunak’s success in quelling the rebellion that had mounted over the weekend, the UK’s former Brexit negotiator, David Frost, said his speech on Monday was a “welcome and reassuring” response. But an ERG member warned “there can be no backsliding” and a senior Foreign Office source said the government was “not interested in Swiss-style, dynamic alignment, Chequers II or any other arrangement that doesn’t respect parliamentary sovereignty in fact and law”. Downing Street insiders pointed the finger at the chancellor for setting hares running. One said: “Everyone is blaming Hunt for speaking to the Sunday Times. But we can’t really do anything about it, other than keep a close eye on him.” Andy Street, the Tory West Midlands mayor, said his region had one of the highest incomes from exports. “Although we are doing what was said – growing our exports to non-EU countries – there is no question that we need the easiest way possible of exporting to what was clearly our biggest market,” he told the Guardian. Trade experts said there were only limited improvements to the flow of goods and services between the UK and EU possible given Sunak’s statement. Prof Anand Menon, of the UK in a Changing Europe thinktank, said: “We’re edging towards an explicit realisation that this is harming the economy but there’s nothing we can do to address that without appearing to betray ‘take back control’.” Switzerland’s relationship with the EU is complicated and the result of many overlapping sectoral deals, so Brussels “wouldn’t want to go around emulating it”, Menon said. He added that while a breakthrough on the Northern Ireland protocol would be significant, any tweaks to the UK’s existing trade deal with Brussels would “make very little difference in terms of macroeconomics”. Jill Rutter, a senior fellow at the Institute for Government, said the UK could try to get the EU to streamline customs processes or deal with the “asymmetry” of border controls but warned Brussels would push back against any perceived “cherrypicking”. Sunak was urged by the head of the CBI to focus instead on resolving the row over the Northern Ireland protocol. “I think the Swiss thing is a complete sideshow,” its director general, Tony Danker, said. “It took them 40 years for Switzerland to have this relationship. We haven’t implemented Boris’s Brexit.” Asked what he made of the progress so far, Danker said: “I don’t think we’re getting anywhere on much. We need to resolve Northern Ireland. “I think that the Europeans, from my conversations, those I speak to say once there’s intent to resolve the Northern Ireland protocol and there’s good will from both sides on that, then everything else comes into play.” Despite Danker’s call for Sunak to be pragmatic about the help a boost of foreign workers could provide, the prime minister said he wanted to focus first on rebuilding public trust in the immigration system given the number of people being smuggled across the Channel. Sunak also used his speech to laud automation and investment in robotics as a way to fuel growth and pay rises. He said that the NHS could be one of the areas to see “radical” innovation. He listed examples of doctors being trained with virtual reality headsets, robots assisting with surgery, and drones transporting prescription medicine to people living in rural areas as ways that robotics is already making a difference in the health service.