David Davis has insisted that Brexit “will not change the kind of country Britain is” as he sought to reassure a European business audience that future regulations would stay broadly aligned with EU rules.

In a speech that went even further than excerpts had suggested to play down the prospect of slashing red tape after leaving, the UK Brexit secretary also emphasised the extent to which many EU rules had been created with British support and encouragement.

The speech to business leaders in Vienna may serve to inflame tensions before a crucial cabinet meeting at Chequers on Thursday, where other Brexit-supporting ministers are anxious to avoid watering down the aims of departure.

Davis acknowledged some symbolic changes were necessary as a result of the referendum, but he echoed recent remarks by Philip Hammond, the chancellor, by suggesting the impact on British society would be limited.

Quick guide What are Brexit options now? Four scenarios Show Hide Staying in the single market and customs union The UK could sign up to all the EU’s rules and regulations, staying in the single market – which provides free movement of goods, services and people – and the customs union, in which EU members agree tariffs on external states. Freedom of movement would continue and the UK would keep paying into the Brussels pot. We would continue to have unfettered access to EU trade, but the pledge to “take back control” of laws, borders and money would not have been fulfilled. This is an unlikely outcome and one that may be possible only by reversing the Brexit decision, after a second referendum or election. The Norway model Britain could follow Norway, which is in the single market, is subject to freedom of movement rules and pays a fee to Brussels – but is outside the customs union. That combination would tie Britain to EU regulations but allow it to sign trade deals of its own. A “Norway-minus” deal is more likely. That would see the UK leave the single market and customs union and end free movement of people. But Britain would align its rules and regulations with Brussels, hoping this would allow a greater degree of market access. The UK would still be subject to EU rules. The Canada deal A comprehensive trade deal like the one handed to Canada would help British traders, as it would lower or eliminate tariffs. But there would be little on offer for the UK services industry. It is a bad outcome for financial services. Such a deal would leave Britain free to diverge from EU rules and regulations but that in turn would lead to border checks and the rise of other “non-tariff barriers” to trade. It would leave Britain free to forge new trade deals with other nations. Many in Brussels see this as a likely outcome, based on Theresa May’s direction so far. No deal Britain leaves with no trade deal, meaning that all trade is governed by World Trade Organization rules. Tariffs would be high, queues at the border long and the Irish border issue severe. In the short term, British aircraft might be unable to fly to some European destinations. The UK would quickly need to establish bilateral agreements to deal with the consequences, but the country would be free to take whatever future direction it wishes. It may need to deregulate to attract international business – a very different future and a lot of disruption.

“Brexit will inevitably mean a change in the way British, Austrian and other European Union companies do business,” Davis said. “It has to, if we are to make good on the referendum result, and carve a path for Britain to strike its own trade deals, have its own immigration policy and make our courts sovereign once more.

“But my message to you, in this room, is that these goals will not change the kind of country Britain is. A dynamic and open country … One leading a race to the top in global standards.”

Hammond was criticised for a similar speech in Davos last month when he suggested regulatory changes would be “very modest”.

“We are taking two completely interconnected and aligned economies with high levels of trade between them, and selectively moving them, hopefully very modestly, apart,” Hammond said.

Expectations are shifting before the Chequers showdown, with Downing Street pushing a vision of “mutual recognition” of regulations and regulators as a way to avoid a hard border in Northern Ireland and minimise trade disruption.

Nonetheless, the Davis speech on Tuesday was a far cry from those who called for Brexit to lead to a bonfire of EU red tape. The Brexit secretary even praised existing systems of regulation, saying Britain had helped design them.

“While we have been a member of the European Union, the UK has been instrumental in the design of its rules,” he said. “Why? Because we are a leading proponent of the rules-based international system.”

Davis also rejected criticism from some former government officials who have privately questioned his grasp of detail and appetite for the hard grind of Brexit negotiations. “I lazily gave up my holiday last summer to sign off on the [Brexit] policy papers,” he told his Viennese audience. “In my lazy schedule I now have got to head off.”

But it was Davis’ less than energetic portrayal of the purpose of Brexit that may pose the biggest challenge to its cheerleaders in cabinet.

In his effort to reassure the EU there would be no “race to the bottom” on regulations, he painted a particularly bleak picture of the liberalised approach sought by fellow Tories such as Jacob Rees-Mogg.

“[Europeans] 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 our history, not our intentions, nor our national interest,” said Davis, despite it featuring heavily as an argument during the referendum campaign.

Instead, he joined a growing group of senior Tory figures to damn the project with faint praise in recent weeks. “It’s a mistake, not a disaster,” said the former prime minister David Cameron in Davos.

Davis also echoed Michael Gove, the environment secretary, who addressed the National Farmers Union conference on Tuesday. Gove has urged Britain to resist pressure from the US for lower food and animal welfare standards.

The coordinated series of speeches by the cabinet’s leading Brexiters could not, however, disguise continuing tension.

Davis argued that European state aid rules should be maintained. “Fair competition means that it cannot be right that a company situated in the EU would be able to be heavily subsidised by the state but still have unfettered access to the UK market, and vice versa,” he said.

But Gove condemned EU rules on state aid, which he said had prevented vital infrastructure investments such as high-speed broadband.

Davis insisted the answer was to emulate mutual recognition agreements negotiated by other EU trading partners, even though Brussels insiders are sceptical these can achieve what Britain hopes.

“The European Union itself has a number of mutual recognition agreements with a variety of countries from Switzerland to Canada to South Korea,” he said.

“Such mutual recognition will naturally require close, even-handed cooperation between these authorities and a common set of principles to guide them. And the certainty that Britain’s plan is a race to the top in global standards – and not a regression from the high standards we have now.”