It has been a busy week for the Hacked Off campaign for a free and accountable press. On Wednesday, Hugh Grant: Taking on the Tabloids, a Channel 4 documentary, was aired on the eve of the Leveson report, and campaign members turned out in force for the publication of the report on Thursday. They later expressed "betrayal" when David Cameron rejected the statutory underpinning suggested by Leveson.

By Friday a group from the campaign were at the Houses of Parliament launching a petition that had already gained 10,000 signatures. It called on David Cameron, Nick Clegg and Ed Miliband to "ignore pressure from media barons and introduce legally backed regulation, independent of politicians and the press, place tighter limits on how much of our media an individual is allowed to own, and promote investigative journalism through effective public interest defences".

By yesterday more than 40,000 people had signed.

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Hacked Off has been an ever-evolving campaign, originally set up by journalism professor Brian Cathcart to push for a public inquiry into press conduct. Much of its public focus has been less about vengeance than preventing what they experienced happening again. Among those launching the petition on Friday was Gerry McCann, the father of missing Madeleine McCann, who said he fully backed the execution of the report.

He added: "For almost all the victims, the reason they were there [at the Leveson inquiry] was to stop other, ordinary people who were caught up in the most unfortunate circumstances suffering unnecessarily beyond what's happened to them."

Hacked Off has seemed to be a double-headed beast: one of its faces that of the wronged celebrity, the other what many might deem the true victims, those who have lost loved ones and, through press invasion, been made to suffer twice over.

There is considerable public sympathy for the family of Millie Dowler, the McCanns and Christopher Jeffries, wrongly depicted in the press as the possible murderer of Jo Yeates.

It is now starting to seem that it would be better for Hacked Off if the celebrities took a back seat and the organisation was allowed to thoroughly metamorphose into a lobby group for wronged members of the general public.

When Charlotte Church mentioned on Question Time last week her own family's suffering at the hands of the press, an audience member said: "Celebrities go out some of the time for notoriety and press, and some of them ask for what they get."

Grant has had relatively little to say since the publication of the Leveson report. On Friday, he appeared on the House of Commons lawn, looking a bit less like a politician and more like a film star once again, but making no statement.

He started a Twitter account, @HackedOffHugh, and within a day gained 32,000 followers. But so far he has sent out only one tweet worth noting "with a group of (non celeb) victims including Hillsborough families listening to PM. Buzzword is betrayal".

Nevertheless, Hacked Off still sees the value of celebrity. On Friday, one of the main contributions came from JK Rowling, a statement, urging people to sign the petition, and expressing her dismay "that the prime minister appears to be backing away from assurances he made at the outset of the Leveson inquiry".

Like most celebrities involved in the campaign, she is most persuasive when she speaks about others who have "suffered the worst, most painful and least justifiable kinds of mistreatment at the hands of the press". But how much more time can many of the highest-profile campaigners give to the cause? Some must now turn their attention to more commercial matters. Next spring Grant starts shooting his first major romcom for some years, while Charlotte Church embarks on a tour in the new year. For them there is more to life than Leveson.