Boris Johnson and other leading cabinet Brexiters have come under renewed attack from business leaders for pushing for a hard Brexit, as a new analysis found the decision to leave the EU was already costing the economy £440m a week.

The foreign secretary, who has been frustrated by the prospect of the UK being tied closely to the bloc, demanded a “full British Brexit” that would allow the country to set its own rules and trade policy.

However, in the latest sign of frustration felt by leading businesses over the lack of progress in Brexit negotiations, the chief executive of Siemens UK called the intervention “incredibly unhelpful” and joined calls for a deal that would not hit the flow of trade between the UK and mainland Europe.

Jürgen Maier said the aim should be “minimum friction” in any future trade deal and chastised the government for presiding over “two years of not having achieved what we were promised, which is that this was all going to be easy”.

“I think the realities are setting in and I think it is time to get away from slogans, ‘full British Brexit’, ‘going into combat with Europe’,” he told BBC Radio 4’s Today programme. “It’s all incredibly unhelpful and what we need to do now is to get closer with our European partners and work out what a realistic, pragmatic Brexit is that works for both sides, the EU and ourselves.”

His intervention follows bleak warnings from Airbus and BMW about their willingness to stay and invest in Britain amid the uncertainty around the future EU trade deal.

Brexiters have begun a renewed attempt to push May into a tougher negotiating stance with Brussels. Johnson has written in the Sun that Britain must not end up with a “bog roll Brexit, soft, yielding and seemingly infinitely long”.

Meanwhile, the international trade secretary, Liam Fox, said the UK was not bluffing about being prepared to abandon trade talks, while the Brexit secretary, David Davis, said there was “lots going on” to prepare for a “no deal” outcome.

With business going public with their concerns, a new analysis suggests British economic growth has been hit by 2.1% so far as a result of the Brexit vote. It equates to a £23bn a year hit to the public finances, or £440m a week. It is in stark contrast to the £350m a week gain promised by the leave campaign. Fox, speaking on the second anniversary of the Brexit vote, said it was essential the EU believed Britain was serious about the threat to walk away from negotiations. “I think our negotiating partners would not be wise if they believed that the prime minister was bluffing,” Fox told the BBC. “I think it’s essential as we enter the next phase of the negotiations that the European Union understands that and believes it.”

His comments came as both No 10 and the Department for Business, Energy and Industrial Strategy sought to play down the prospect of the UK failing to secure a deal with the EU, after the aeronautics company Airbus confirmed it was considering cutting thousands of jobs in the UK in the absence of more detail about post-Brexit trading arrangements.

Writing in the Sun, Johnson said the public were keen to get on with breaking away from Brussels. “Across the country I find people who, whatever they voted two years ago, just want us to get on and do it,” he said.

“They don’t want a half-hearted Brexit. They don’t want some sort of hopeless compromise, some perpetual push-me-pull-you arrangement in which we stay half-in and half-out in a political no man’s land, with no more ministers round the table in Brussels and yet forced to obey EU laws. They don’t want some bog-roll Brexit, soft, yielding and seemingly infinitely long. They want this government to fulfil the mandate of the people and deliver a full British Brexit.”

In its risk assessment, published on Friday, Airbus said no deal would be “catastrophic” and it would “force Airbus to reconsider its footprint in the country, its investments in the UK and at large its dependency on the UK.”

The Treasury has earmarked £3bn for Brexit contingency planning, with half only made available in 2019-20, but Brussels is said to have taken the view that the UK is making no credible preparations for the prospect of a no-deal Brexit in 10 months’ time.

In a speech last month, the UK’s former EU ambassador Sir Ivan Rogers said the UK had still not set up any of the independent regulatory bodies that would be needed in the event of no deal.

“The fact that, in so many areas, we are obviously not doing that … is yet another reason why the EU side has long since concluded that the UK would not walk out,” he said.

Jenny Chapman, the shadow Brexit minister, said Fox’s comments were “the height of irresponsibility” in the wake of the Airbus risk assessment. “The next time Liam Fox parrots the slogan ‘no deal is better than a bad deal’ he should give some thought to the 14,000 people who work for Airbus, and the thousands of other people who have jobs dependent on trade with Europe,” she said.

In the interview, Fox also put down a marker of resistance over any future plans to keep the UK in a single market for goods, saying such a scenario “wouldn’t be acceptable to me”.

Whitehall sources have suggested a compromise is “100% the direction of travel”, believing the UK would go some way to maintaining a frictionless trading relationship if it sticks to single market rules on manufactured products but diverges elsewhere, such as on services.

Fox said the deal would imply an acceptance of free movement of people, which he said had been rejected by the public in the referendum and would be likely to mean oversight by the European court of justice.

“My main reason for voting to leave was that I think that we should not be subjected to the jurisdiction of a foreign court,” he said.

He said he was unconcerned by the apparent lack of progress, including the inability of May’s cabinet to reach a consensus on future customs arrangements.

“I’ve always thought that most of the actual negotiation would get done closer to the point of exit rather than early on in the process,” he said. “No big negotiations get settled early on in the process.”

Fox’s comments came as the former US presidential candidate Hillary Clinton expressed her view about a breakdown of Brexit negotiations. The former secretary of state, speaking at Trinity College Dublin, said she continued to believe in the value of the EU.

“No matter the outcome of these discussions, Brexit should not be allowed to undermine the peace that people voted, fought and even died for,” she said.