Sunak told business leaders at a Confederation of British Industry (CBI) conference he was "unequivocal" that Britain should pursue its own agenda on regulation and migration.
Earlier, the CBI said Britain should create a programme of temporary work visas to boost economic growth and also resolve a dispute with the EU over trade rules in Northern Ireland.
"On trade, let me be unequivocal about this: under my leadership, the United Kingdom will not pursue any relationship with Europe that relies on alignment with EU laws," Sunak said.
Britain's grim economic outlook, marked by stagnant business investment and sluggish post-Brexit trade, has sparked talk from businesses and economists of closer ties with the EU and a more relaxed approach to immigration as easy ways to boost growth.
Finance minister Jeremy Hunt last week said he was confident Britain would be able to remove "the vast majority" of barriers to trade with the EU, without rejoining its single market.
On Monday, Sunak struck a different tone.
He said Britain's exit from the EU had helped bring more flexibility on business regulation and had been necessary to secure "proper control" of the country's borders.
"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.
Sunak emphasised the need to tackle illegal immigration to build trust in Britain's migration system - one that he hoped would be a beacon for talent around the world.
Speaking minutes earlier on the same stage, CBI Director General Tony Danker said businesses were suffering labour shortages that could be addressed with a better immigration system.
"We don't have enough Brits to go round for the vacancies that exist, and there's a skills mismatch in any case," Danker said.
"Let's have economic migration in areas where we aren't going to get the people and skills at home anytime soon. In return, let's make those visas fixed-term," Danker said.
Danker also called on the government to sort out a dispute with the EU over how the bloc's rules should apply in Northern Ireland, which prompted the EU to suspend cooperation in areas such as scientific research.
"I say to Brexiteers, the best guarantor of Brexit is an economy that grows. Its biggest risk is one that doesn't," Danker said.
Last week Britain's budget watchdog said the country was already probably in recession, and gave a subdued medium-term growth forecast which showed a greater reliance on immigration to boost output than it had predicted earlier this year.