Theresa May is not bluffing when she threatens to take the UK out of the European Union without a deal, a senior cabinet minister has said.

Liam Fox, the international trade secretary, said the prime minister was ready to walk away without an agreement as part of her commitment to deliver a “people’s Brexit”.

The government is committed to its policy of “no deal is better than a bad deal”, he added, telling the EU it needs to “understand that and believe it”.

His warning comes as cabinet ministers battle for control of the Brexit process ahead of a key meeting at Chequers next month.

The “away day” of the cabinet’s Brexit subcommittee is designed to resolve a number of major differences between senior ministers on issues such as the single market, customs union and the Northern Ireland border.

Discussions are likely to include how much the UK should compromise in order to avoid crashing out of the EU without a deal.

Mr Fox told the BBC: “The prime minister has always said that nothing is agreed until everything is agreed and that no deal would be better than a bad deal. I think it’s essential as we enter the next phase of the negotiations that the European Union understands that and believes it.

He added: “If we were to leave, the economic impact on a number of European countries would be severe. Countries like Ireland, countries like the Netherlands, countries like Belgium would really feel the impact of that and that cannot be what the European Union 27 actually want to see.

“This ultimately has to be about an economic and a people’s Brexit, not a bureaucrat’s Brexit.

“I think our negotiating partners would not be wise if they believed that the prime minister was bluffing.”

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Mr Fox was backed by foreign secretary Boris Johnson and Brexit secretary David Davis in a round of media appearances by Brexiteer cabinet ministers.

Asked about the prospect of leaving without a deal, Mr Davis told The Express: “We don’t want to do that, never have. The best option is leaving with a good deal, but you’ve got to be able to walk away from the table.

He also dismissed accusations the government had not properly prepared for Brexit, saying: ”There’s lots going on, we haven’t made it public for very simple reasons.

“This is a careful process, it is not designed to scare the horses to worry people, it is designed to get the work done.”

And writing in The Sun, Mr Johnson said: “Across the country I find people who – whatever they voted two years ago – just want us to get on and do it.

“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.”

Airbus CEO warns the company could leave the UK in the event of no deal Brexit

He said: “I completely understand when companies say they rely on efficient mobility as it currently stands, raising concerns that restricting people’s ability to travel at short notice would be as damaging to our economy as frictions and disruption at our borders.”

His comments came after leading businesses said growing uncertainty over Brexit risked thousands of UK jobs being moved abroad.

Airbus said it was considering cutting thousands of jobs in the UK as it starts to “press the button on crisis actions” over Brexit concerns.

Katherine Bennett, the company’s senior vice president in the UK, said: “We don’t deal in idle threats. We seriously believe a no-deal Brexit would be catastrophic.”

And Juergen Maier, chief executive of Siemens UK, said the language used by Mr Johnson and other Brexiteers was “incredibly unhelpful”.

He told BBC Radio 4’s Today: “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’.