Boris Johnson said he was "obviously very concerned" about the findings of the inquiry into the BBC’s Martin Bashir interview with Princess Diana.
The prime minister also said he hoped the national broadcaster "will be taking every possible step to make sure that nothing like this ever happens again".
He made his comments as Scotland Yard said it would assess the contents of the investigation by Lord Dyson to ensure there is no "significant new evidence" to support a criminal investigation.
Speaking during a visit to Portsmouth, the Prime Minister said: "I’m obviously concerned by the findings of Lord Dyson’s report – I’m very grateful to him for what he has done.
"I can only imagine the feelings of the royal family and I hope very much that the BBC will be taking every possible step to make sure nothing like this ever happens again."
The Metropolitan Police said in a statement: "Following the publication of Lord Dyson’s report we will assess its contents to ensure there is no significant new evidence."
Justice Secretary Robert Buckland told Sky News the report "raises some very serious questions" and "issues around governance" within the BBC.
He said: "I think an apology is a start, but I don’t think it’s the end of it."
Home Secretary Priti Patel said: "With a free press and free media, the media themselves and our broadcasters, and the national broadcaster, has a huge sense of responsibility with the way in which they investigate, review and conduct their own media reports.
"So there will be very, very strong and searching questions for the BBC post the publication of this report."
Culture Secretary Oliver Dowden last night said the report "reveals damning failings at the heart of the BBC" and he will "consider whether further governance reforms are needed".
Prince William and his brother Harry have both criticised the corporation’s failures surrounding the Panorama interview with their mother, with the Duke of Cambridge saying it "contributed significantly to her fear, paranoia and isolation".
Tory former leader Sir Iain Duncan Smith told Sky News’ All Out Politics programme: "In the beginning there was clearly a fraud that took place to secure an interview and that in itself I think the director of public prosecutions may need to think further on that one."
He was also critical of the cover-up by the BBC arguing had the initial investigation been properly carried out "history may have been changed by it".
He added: "They were trying to kill news, which is not what they are about.
"A news broadcaster must follow the news, whether its news about their organisation or news about some other organisation.
"So this requires some rethinking about the nature of how the BBC works I think."
Mr Bashir had faked bank statements, which was a "serious breach" of BBC guidelines on straight-dealing, as he showed them to Diana’s brother Earl Spencer to gain access to her, the inquiry by Lord Dyson concluded.
He has since stepped down as the BBC’s religion editor due to ongoing health issues.
Despite his ill health, he and the BBC have apologised over the report’s findings, with Mr Bashir describing his decision to fake the bank statements as a "stupid thing to do" and "an action I deeply regret".
But he claimed it had "no bearing whatsoever on the personal choice by Princess Diana to take part in the interview".
The Panorama programme, which aired in November 1995, was watched by 23 million people.
Diana was killed in a car crash in Paris at the age of 36 two years later.
In a video statement responding to the Dyson report, Prince William said the interview had "effectively established a false narrative which, for over a quarter of a century, has been commercialised by the BBC and others".
He called for it never to be broadcast again, adding: "This settled narrative now needs to be addressed by the BBC and anyone else who has written or intends to write about these events."
Prince Harry said in his response: "Our mother lost her life because of this, and nothing has changed."
Former BBC director-general Lord Hall, who was director of news at the time, said Mr Bashir and his team’s actions "fell short of what was required".
The corporation’s current director general, Tim Davie, said: "While today’s BBC has significantly better processes and procedures, those that existed at the time should have prevented the interview being secured in this way.
"The BBC should have made greater effort to get to the bottom of what happened at the time and been more transparent about what it knew.
"While the BBC cannot turn back the clock after a quarter of a century, we can make a full and unconditional apology. The BBC offers that today."