Khosrowshahi added: "None of this should have happened, and I will not make excuses for it".
"Deliberately concealing breaches from regulators and citizens could attract higher fines for companies", James Dipple-Johnstone, deputy commissioner of the UK Information Commissioner's Office, said in a statement.
Khosrowshahi, meanwhile, is offering free credit monitoring for drivers whose personal info was stolen in the hack and has hired security expert Matt Olsen, a former staffer at the National Security Agency and director of the National Counterterrorism Center to help the company going forward.
There, hackers found the username and password to access Uber user data stored in an Amazon server.
Theresa May's official spokesman said: "These are obviously concerning reports and the National Cyber Security Centre is working closely with domestic and global agencies, including the National Crime Agency and the Information Commissioner's Office, to investigate if and how this breach has affected people in the UK".
"While I can't erase the past, I can commit on behalf of every Uber employee that we will learn from our mistakes", Khosrowshahi, who took over as chief executive at Uber in August, said in the breach post.
Company bosses have now admitted covering up the breach - but what exactly happened?
Tuesday's data breach revelations are yet another setback for Uber, a private company that is valued at about $70 billion.
State Attorneys General from NY and MA have opened investigations into the data breach.
Uber is seeking to mend fences in Asia after having run-ins with authorities, and is negotiating with a consortium led by Japan's SoftBank Group for fresh investment.
Uber also fired two employees who were responsible for providing information to hackers.
"When we learned of the incident in November 2016, we took steps to contain and prevent harm, but we did not let drivers know". "I've opened up an investigation to take a look at it".
Forensic analysis confirmed that the names and driver's license numbers of around 600,000 U.S. drivers, as well as personal information about 57m users - including names, email addresses and mobile phone numbers - had been compromised.
Mr Kalanick, through a spokesman, declined to comment. However, the information has now been revealed after the tech company's new CEO, Dara Khosrowshahi, opted to publicly announce it in a bid to reassure users he was making big changes.