UK prime minister Rishi Sunak has ruled out any Swiss-style alignment with EU laws in order to strike a trade deal with the bloc, instead promising that the existing Brexit arrangements could “deliver enormous benefits for the country”.

Talking at the CBI annual conference in Birmingham on Monday, Sunak came under pressure to address two key business demands to open up trade with the EU and allow greater immigration to tackle labour shortages.

Downing Street has been forced to play down reports over the weekend that the UK was considering a Swiss-style trade relationship with the EU.

Sunak said: “Let me be unequivocal. Under my leadership, the UK will not pursue any relationship with Europe that relies on alignment with EU rules. I voted for Brexit. I believe in Brexit. Brexit can deliver enormous benefits and opportunities for the country.”

He pointed to migration as one of the areas in which the UK has benefited from Brexit, saying that “we have proper control of our borders . . . we are in control”.

Business regulation would also improve after leaving the EU, he said. “We need regulatory regimes that are fit for the future, that ensure that this country can be leaders in those industries that are going to create the jobs and the growth of the future. And having the regulatory freedom to do that is an important opportunity of Brexit.”

Sunak said that the UK could now strike trade deals elsewhere, pointing to talks to sign up to the Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP), which could open up tariff-free trade with countries in the Indo-Pacific.

With the opposition Labour party on a charm offensive to win over British industry, Sunak promised that the Conservatives would remain the party of business: “It’s business that creates wealth and jobs that the country needs. There is lots more that [the government] can do.”

Talking before the prime minister, CBI chief Tony Danker called for Sunak to focus on the economic needs of the country over political “barriers”, including allowing more immigration to alleviate labour shortages and improving trade with the EU.

Danker told ministers that they should also introduce tax incentives to support investment in the UK to offset the rise in corporation tax to 25 per cent.

As chancellor, Sunak had consulted on a replacement scheme to the super deduction allowance, which allows tax breaks on capital spending, that ends in April.

But on Monday the prime minister ducked questions about whether he would consider a new investment incentive to replace the super deduction allowance next year, pointing instead to existing schemes such as the annual investment allowance.

Sunak promised to “fire up the innovation engine” of the UK, and pledged support for innovative businesses and entrepreneurs.

Chancellor Jeremy Hunt last week signalled a new government industrial focus on five key industries: digital technology, life sciences, green industries, financial services and advanced manufacturing.

Hunt also committed to maintaining levels of government research and development spending, but shocked the start-up community by slashing widely used small business tax allowances that have helped boost innovation in the UK.

Tech founders and science chiefs have attacked the plans — which were billed as an attempt to reduce misuse of the system — as a backward step if the UK is serious about wanting to develop companies in important industries.

On Monday, Sunak said that the UK would have the “world’s most attractive visa regime” for entrepreneurs and skilled tech workers.

He also committed to setting out plans to help energy intensive businesses, with government support due to end in March next year. But he said that the help would be targeted at those who need the most support.

Sunak said that he knew how “tough” it had been for energy intensive businesses. But he added that it was “right and responsible to adjust how that support works. It will be more targeted at those businesses that need our help.”

He added: “We recognise a particular issue with a group of industries who are very reliant on energy that we need to make sure we have a plan for and you can expect the chancellor to address that.”