European Union countries’ fears that Britain will start a “race to the bottom” on taxes and standards when it leaves the EU are “based on nothing”, the Brexit Secretary is to claim.

David Davis is travelling to Austria where he will attempt to reassure an audience of local business leaders that the UK will not try to undercut the EU after it leaves.

His speech will come after a recent slide presentation from the European Commission, presented to member states, which suggested that the UK may reduce “levels of occupational safety and health” after Brexit – leading to “higher exposure to chemicals and carcinogens”.

In the same presentation the commission also said it expected reduced “informational and consultation rights for workers” in order to reduce “delays for collective dismissals” after Britain left the bloc.

Mr Davis will tell business leaders: “I know that for one reason or another there are some people who have sought to question [whether we will maintain standards after the UK leaves].

“They fear that Brexit could lead to an Anglo-Saxon race-to-the-bottom, with Britain plunged into a Mad Max-style world borrowed from dystopian fiction.

“These fears about a race to the bottom are based on nothing, not history, not intention, nor interest.”

The Chancellor, Philip Hammond, warned last year that if the UK did not get a trade deal it “could be forced to change our economic model and we will have to change our model to regain competitiveness”.

He later clarified that unfair competition on tax and regulation was “neither our plan nor our vision for the future”, suggesting the UK economy would stay “recognisably European”.

Mr Davis will on Tuesday try to unpick more of the damage done by Mr Hammond’s comments, and suggestions by some Brexiteers such as Jacob Rees-Mogg that taxes should come down after Brexit.

The Brexit Secretary will tell business leaders that the UK “will continue our track record of meeting high standards after we leave the European Union”.

He will continue: “That’s why it’s a message delivered by every member of Britain’s Government as we meet our European counterparts.

“Whether it’s Theresa May committing to maintaining and enhancing workers’ rights; the Chancellor’s powerful advocacy for the stability of the European banking system; Michael Gove’s crusading zeal for improving animal welfare and environmental outcomes; or my friend the Foreign Secretary, who explained in an important speech last week how Brexit could be used to distinguish between membership of EU institutions and our shared European culture, values, civilisation.”

Reacting to the trailed parts of the speech, Liberal Democrat leader Vince Cable said Mr Davis “might as well be making the case for staying in the EU”, while Labour backbencher Chuka Umunna said that “not everyone in the Cabinet” agreed with Mr Davis that there would be no race to the bottom.

“Theresa May has repeatedly failed to rule out scrapping working time regulations, Boris Johnson wants to get rid of the social chapter, and Liam Fox says he’s in favour of importing chlorinated chicken from the United States,” he said.

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“In reality, the best way to protect and enhance the high standards that exist in this country is to stay in the single market and the customs union.”

Officials on both sides are being tight-lipped about this week’s resumption of face-to-face Brexit, which are talking place in Brussels. A previous round a week ago ended in recriminations after Mr Davis and Mr Barnier came to verbal blows about the UK’s position on the enforcement of EU rules.