The revelations about Facebook and Cambridge Analytica have marked a "turning point" in people's attitudes to their online data, the UK's Digital, Culture, Media and Sport Secretary, Matt Hancock, said.
The Digital, Culture, Media and Sport Secretary said he understood why people were deleting their accounts with the social media giant and promised the Information Commissioner would also be given beefed-up powers.
But the data watchdog has yet to be granted a warrant to search CA's computers as part of its current investigation and Mr Hancock acknowledged the "system isn't good enough" at present.
A High Court judge in the UK adjourned the Information Commissioner's Office (ICO) application for a warrant until Friday.
Mr Hancock told a Westminster lunch: "After this week's revelations I think it is time that social media platforms come clean with what data they really hold on people."
He added: "I have actually been worrying for quite some time about this sort of problem.
"We didn't know the details of the revelations that came out at the weekend but the Information Commissioner already had an investigation to get to the bottom of these sorts of problems.
"It is clear to me that the rules need to be strengthened to make sure that she has the enforcement powers that we need."
Facebook's boss Mark Zuckerberg said it was a mistake to rely on CA to delete tens of millions of Facebook users' data, as he apologised for the "major breach of trust".
He said the political consultancy had provided formal assurances that information harvested from 50 million profiles had been destroyed after Facebook first learned of the breach in 2015.
Mr Zuckerberg set out a series of measures to toughen up the site's policies, said he was now open to Facebook being regulated, and accepted that malign actors were trying to use the social network for political ends.
But the Culture Secretary said it should not be up to individual sites to decide how to respond as he highlighted plans to strengthen data law.
Mr Hancock, who has faced privacy concerns over his own social media app for constituents, said the Data Protection Bill would strengthen the rules.
"I think this week has marked a turning point in people's attitude towards the big platforms," he said.
"You can't just let the companies decide what is the balance between privacy and use of data and innovation. That is a decision for society, reflected in the laws that we pass here."
Facebook has seen billions of US dollars wiped off its market value following the row involving CA, which is accused of using the data to help Donald Trump's US presidential campaign target political ads on the platform.
The company has denied using Facebook data in its work on the campaign and added: "We're committed to being responsible, fair and secure with data.
"We'll be working with everyone - Facebook, independent auditors and the ICO - as their investigations continue."
The scandal has prompted calls from politicians on both sides of the Atlantic for Mr Zuckerberg to answer to them in person for the breach and led to an online campaign for people to delete their profiles.
Mr Hancock said: "Of course I understand why people are deleting Facebook accounts.
"Without trust people will understandably continue to remove their Facebook accounts and without transparency over how data is used there can be no trust."
On Wednesday, Mr Zuckerberg made his first public statement since the controversy erupted - via a Facebook post.
Journalists at the Guardian had told Facebook in 2015 that Aleksandr Kogan, a Cambridge University psychology researcher, had shared data from an app he had developed with CA, he said.
Facebook immediately banned Dr Kogan's app and demanded that he and CA delete the data, for which they provided "certifications" that they had, the boss said.
Last week, the company was alerted by the Guardian, the New York Times and Channel 4 that CA may not have deleted the data as they had said and the firm was banned from Facebook.
The personality survey created by Dr Kogan - who claims he has been made a "scapegoat" by Facebook and CA - was installed by about 300,000 people, Mr Zuckerberg said.
Facebook's settings at the time allowed developers to access the personal data of not just the people who used their app, but of all of their friends as well - leading to information being gathered on tens of millions of people.
Facebook will now ban developers who do not agree to an audit, and an app's developer will no longer have access to data from people who have not used that software in three months.