Hugh Grant says the closure of the British tabloid News of the World is a "watershed moment" in the battle against unethical journalism.

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The newspaper's owners announced Thursday they are ceasing publication after it became public some of their reporters illegally accessed the phones of people, including a missing 13-year-old girl, who was ultimately found dead.

"This is the watershed moment when, finally, the public starts to see and feel, above all, just how low and how disgusting this particular newspaper's methods were. And what will emerge shortly is that it wasn't just this newspaper," Grant told CBS News' "The Early Show."

The "Four Weddings and a Funeral" and "Bridget Jones's Diary" actor went on to say "pretty much all" of the British tabloids "were keen phone hackers."

Grant is among the celebrities who fell victim to illegal phone hacking at the hands of tabloid journalists. Others affected reportedly include Prince William and entertainers Mick Jagger, Eric Clapton and Gwyneth Paltrow.

Grant wrote an article voicing his outrage at the scandal in The New Statesman.

In his interview with CBS News, he called the circumstances an "enormous national scandal."

"The politicians will for sure try to push it into the long grass. They're going to say, 'We'll let the police do their inquiry and we won't have a proper, full public inquiry in the meantime.' But that's what we need," Grant said.