Dozens of Britons who believe their phones were illegally tapped by journalists have written to Prime Minister David Cameron urging him to consider tighter press regulation.

Celebrities, including actor Hugh Grant and Jude Law, were among 60 people who signed the open letter, which expressed alarm at news reports that Cameron will reject press regulation proposals from the Leveson inquiry, the investigation into Britain's media ethics.

The letter, which calls for an end to self-regulation by the press, asks for assurances that Cameron will consider recommendations from the inquiry with an open mind.

The inquiry was set up in the wake of the phone hacking scandal, which exposed widespread illegal behaviour across the industry.

Cameron told the BBC Sunday he wants to improve press practices but rejects "heavy-handed state intervention."