They may sound an unlikely duo – former Coalition prime minister Malcolm Turnbull and trade unionist Sharan Burrow – but they’re to work together.

As co-chairs of the the Australians for a Murdoch Royal Commission lobby group, they take up the campaign for an inquiry into Rupert Murdoch's local media operations.

Former prime minister Kevin Rudd, who established the group, is stepping aside from the organisation as the role is seen as inconsistent with his new role as Australia's ambassador to the US.

In a report, The Age and the Sydney Morning Herald say Turnbull believes the Coalition needs to address its relationship with News Corp if it hopes to win office again. He has urged Opposition Leader Peter Dutton to distance his party from Sky News to boost its electability, saying the party he once led had been in “coalition” with News Corp.

In an opinion piece for the Nine Entertainment newspapers, Turnbull and Burrow argue that revelations in the Dominion Voting Systems case of Fox News’ on-air talent indulging former president Donald Trump’s “stolen election” lies “justify the rigorous inquiry that only a royal commission can bring”.

“The Foxification of Australia won’t be halted by piecemeal media reforms that can’t pass parliament unless they are signed off by Rupert,” he said.