Labour deputy leader Harriet Harman said today her party would have a mandate to "follow through on Leveson" if it won the general election in May.
"We are absolutely committed to what Leveson proposed and we do not think that business as usual is acceptable," she told a rally organised by Hacked Off.
Comedian John Cleese spoke at the same event and likened journalists arguing for self-regulation to murderers wanting to police themselves.
The Monty Python star also said that Britain's newspaper editors were cold-blooded liars who only wanted control to remain fully within the industry so they could be "free to do what they damn well like".
Tweets about Cleese's comments during the Hacked Off event in Parliament angered campaigners, leading to a terse confrontation during the meeting with the journalist, Alex Wickham from the Guido Fawkes website, who posted them.
The issue of press regulation has yet to be fully resolved despite Lord Justice Leveson's exhaustive inquiry into the culture, practices and ethics of the press following the phone-hacking scandal.
Cleese accused the press of "monstrous behaviour", which at times was "sociopathic", and told the rally: "Of course they want to regulate themselves, we'd all like to regulate ourselves wouldn't we?
"Builders, accountants, murderers, they'd all like to regulate themselves."
He added: "The murderers would make a very good case – they'd say we murdered a lot of people, we know people who have murdered people. We really are best qualified to regulate …"
Cleese dismissed claims that changes would muzzle the press as "crap", citing a long list of high profile figures who have publicly put their name to calls for reform.
"It's hard to tell how much of this is bare-faced cynical lying and how much is ignorance," he said.
"In the case of editors, I think it's almost entirely cold-blooded lying."
After reporter Wickham tweeted about Cleese's comments on murderers, Hacked Off associate director Evan Harris told the meeting he was going to "call out" the journalist.
This is very weird RT @MediaGuido: John Cleese compares journalists to murderers: "murderers would like to regulate themselves too"
— Alex Wickham (@WikiGuido) February 25, 2015
One member of the rally called the reporter a "cretin" while others questioned how he could sleep at night.
Harris asked for the journalist to "speak up a bit so we people can hear your explanation" but went on to tell him to sit down as he was not going to give him the "dignity of a platform".
Hacked Off staged the event, held in a committee room in the House of Commons, to ensure that press reform "remains on the political agenda" ahead of the general election.