City regulators including the PRA have come under fire in recent years for burdening companies with too much red tape, leading to criticism that they are hampering economic growth.
The Financial Conduct Authority (FCA) has also faced scrutiny for introducing too many rules and regulations.
In February the FCA was criticised for plans to “name and shame” companies under investigation and also faced complaints over rules forcing companies to disclose their diversity and inclusion policies.
Jeremy Hunt, the former chancellor, last year introduced a new secondary objective for regulators, including the PRA and the FCA, forcing them to consider economic growth as a “secondary objective”.
The move was widely viewed as a tacit criticism that the City’s regulators had become a drag on the economy and were standing in the way of growth.
Since taking power, Sir Keir Starmer has largely followed the previous government’s plans, forcing regulators to think more about how their decisions affect economic growth.
On Monday he told an audience of international financiers at the International Investment Summit that the government would force economic regulators to “take growth as seriously as this room does”.
Mr Woods, whose PRA regulates 1,500 banks, building societies and insurers, said getting the right balance was difficult but added it was “implausible” that good businesses could “ thrive in an environment of ever-expanding regulation”.
He pointed to the PRA’s decision to abolish the bankers’ bonus cap as a sign that regulations could be rolled back, saying the cap had been “damaging to competitiveness”.
Mr Woods said: “Getting rid of it was an important early signal of intent, that we are serious about changing regulations where they don’t do something useful and are bad for competitiveness and growth.”
Nikhil Rathi, chief executive of the FCA, also told the same event that his regulator had found the new growth objective “liberating”.
“We are now having a much needed, more candid conversation about our collective risk appetite,” he said.
David Postings, chief executive of bank lobby group UK Finance, added: “If we can collectively get the balance right between risk and protection for consumers, then this will help in supporting economic growth and financial inclusion in the UK,” he said.