The watchdog also would get the power to solve pricing disputes between online platforms and news publishers to ensure media companies get paid fairly for their content, the government said.
Tech companies would face fines worth up to 10% of their annual global revenue for breaking the rules, which for the biggest companies would amount to billions of dollars.
Google and Meta did not respond immediately to requests for comment.
The U.K. rules are on top of a separate online safety law that is in the works, which would give users more power to block anonymous trolls and step up requirements for digital platforms to take down illegal material like posts involving child sexual abuse or terrorism.
The European Union has similar laws in the pipeline. The 27-nation bloc's Digital Services Act will require big tech companies to police their platforms more strictly for harmful or illegal content and services, while its Digital Markets Act is aimed at reining in online "gatekeepers." Both threaten big fines for violations.