A Cabinet minister has denied a report that Rishi Sunak’s Government is considering putting the UK on the road to a Swiss-style relationship with the EU.

The Sunday Times reported the move could take place over the next decade as the Government eyes up a closer relationship with the EU that avoids the current barriers to trade.

Any such shift, only a few years after Boris Johnson secured a deal with the EU after years of back-and-forth negotiations, would likely inflame backbench Tory Brexiteers.

Downing Street sources on Saturday evening had rejected the report, with Health Secretary Steve Barclay echoing that on Sunday as he toured broadcast studios.

The former Brexit secretary told Sky’s Sophy Ridge on Sunday programme he did not recognise such a report.

The Times suggested that – behind closed doors – some in Government have indicated the pursuit of a frictionless trading relationship with the bloc requires moving to a Swiss-style arrangement over the next 10 years.

According to the paper, this would not extend to a return to freedom of movement.

“We’ve got a Prime Minister who himself supported Brexit. I myself did and was Brexit secretary, and worked very hard to maximise our control of our laws, our borders and our money,” Mr Barclay said.

“So, it’s absolutely important, particularly in those high-growth sectors, such as financial services, life sciences and the green industries, that we really use the Brexit freedoms we have.

“So, I don’t recognise this story at all.”

Asked if he could support a Swiss-style relationship, he said: “Well, I didn’t support that. I want to maximise the opportunities that Brexit offers.”

Switzerland and the EU have a close economic relationship based on a series of bilateral agreements, giving the country direct access to parts of the EU’s internal market including the free movement of people.

The UK is locked in long-running talks with the EU over the Northern Ireland Protocol, a post-Brexit arrangement for the region designed to avoid a border on the island of Ireland.

Unionists have opposed the protocol as impeding trade between Northern Ireland and Great Britain, placing a border in the Irish Sea.

This has resulted in the collapse of the Stormont Assembly, with top civil servants left to run government departments.

However, there have been renewed hopes in recent weeks that a deal can be secured and the relationship improved between the UK and the EU after years of tensions.

A Swiss-style veterinary agreement has been one of the options mooted by some on the EU side as a solution to the protocol dispute, while in the years after the Brexit vote a deal inspired by the Swiss-EU relationship was seen as one among many options for the UK after it voted to leave the bloc.

Chancellor Jeremy Hunt this week admitted that Mr Johnson’s Brexit deal caused damaging trade barriers with the European Union, as he said immigration will be “very important” for the economy.

Mr Hunt also insisted the UK would find a way to improve trading ties with the EU without rejoining the single market.

On Sunday, former work and pensions secretary Chloe Smith said that seeking a new Swiss-style arrangement would not be a “wise path” for the Government.

“I don’t think that would be a particularly wise path at this time,” she told Times Radio.

“I think that the government has actually responded already this morning to those particular ideas, and I don’t believe that’s one that’s been taken forward.”

Simon Clarke, the former levelling up secretary, was also among those to criticise the idea.

The Tory MP tweeted: “I very much hope and believe this isn’t something under consideration. We settled the question of leaving the European Union, definitively, in 2019.”

Lord Frost, the former chief Brexit negotiator, also tweeted that he hoped if the report was correct, “the Government thinks better of these plans, fast”.

Shadow work and pensions secretary Jonathan Ashworth told Sky News that Labour does not want to rejoin the EU single market nor would it seek to adopt a Swiss-style set of arrangements.

He said: “We’re not proposing returning to the single market or the customs union, or anything like that.

“But we do want to negotiate a bespoke deal for the United Kingdom, so that our businesses can export, so that we can get those agreements on agriculture, so we can work together on security issues.”