Hugh Grant is starting to annoy people. “Who does the guy think he is?” one exasperated shadow cabinet member asked me. “Ed’s basically been out there, he’s taken a huge political gamble on hacking, and Grant is threatening all sorts if we don’t sign up to every dot and comma of Leveson.”

Another Labour MP expresses similar frustrations about Hacked Off, the actor’s anti-News International campaign vehicle. “When they were going out front with the Dowlers they had the public with them. Since they’ve started focusing on the celebrities, people are starting to switch off. It’s been a strategic mistake.”

There is growing wariness in Labour ranks about where the phone-hacking debate is heading. So far it has proved the making of Ed Miliband. It transformed perceptions of his leadership, unsettled David Cameron to the extent that questions were asked about his political survival and placed a series of judicial time bombs under the coalition.

Part of the concern for Labour is that the issue of a new regulatory regime for the British media is very clearly on Cameron’s radar. Recent months have brought a sudden stiffening of the Tories’ position on Lord Leveson and his inquiry. Even the Prime Minister has started making ambiguous noises when asked if he will implement the findings in full. “We don’t want heavy-handed state intervention,” he said last month. “We’ve got to have a free press; they’ve got to be free to uncover wrongdoing, to follow the evidence, to do the job in our democracy they need to do.”

Then there was the surprise promotion of Jeremy Hunt to Health Secretary in September’s cabinet reshuffle, a calculated V-sign to those who had claimed revelations of Hunt’s proximity to News International had ended his political career. And on Sunday, Eric Pickles, the Communities Secretary, made a well-timed intervention on Sky News. “We should be very, very, very reluctant to take on legislation,” he said. “It’s a balance and my view is that we should always balance in favour of a free press.”

There is alarm in the shadow cabinet that Labour is being forced down a cul-de-sac and has no strategic endgame. With the public interest in phone-hacking dissipating, the worry is that the Tories will outmanoeuvre Labour by signing up to parts of Leveson but stopping short of full statutory regulation.

That scenario does not just give Labour presentational problems: some MPs baulk at the prospect of fighting the next election with a manifesto commitment to introduce stiff regulation and therefore bringing the party into conflict with the press.

Red lines

Miliband is alive to the danger and has despatched Harriet Harman to open up a “one-on-one dialogue” with various newspaper editors to identify “red-line” areas. Harman is said to ensure that the discussions include a reminder that she once got prosecuted for leaking sensitive information to the media.

In truth, Miliband’s room for manoeuvre is limited. He has placed great store by his determination to bring a feral press pack to heel. His trusted lieutenant Tom Watson has informed him that he for one will entertain no backsliding from the party in this matter. And Hacked Off still has the leader’s ear.

When I spoke to members of the campaign shortly after they’d met Miliband at the Labour conference, they said he had left them confident he would implement Leveson in full.

Hugh Grant may well be starting to annoy people but he still has the capacity to influence them. And if the Tories are ushering Labour towards a Leveson-inspired cul-de-sac, Miliband appears to have little choice but to walk into it.