James Murdoch’s continued role in his father’s media empire is sufficient reason for the proposed takeover of Sky by 21st Century Fox to be blocked, say Ed Miliband and Vince Cable.

Allegations were heard in the high court against News International in which the role of Murdoch’s son in the alleged deletion of incriminating emails was raised in evidence, the two men say. Miliband and Cable also point out that a 2012 Ofcom report was “withering about the conduct of James Murdoch” when it examined the last attempted take over of Sky, and they urge the culture secretary, Karen Bradley, to immediately refer the issue to the watchdog again.

James, the younger son of Rupert Murdoch, stood down as chairman of BSkyB in 2012 as Ofcom escalated its investigation into whether he was a “fit and proper person” to be in charge in the wake of the phone hacking scandal. In a joint article published in the Observer, the former Labour leader and the former Liberal Democrat business secretary write: “The question as to whether 100% ownership is right now when it was not four years ago can be answered emphatically: no.

“James Murdoch, despite what the 2012 report said, is now back as chairman of Sky and is chief executive of 21st Century Fox as it seeks to take over Sky. There are crucial – unanswered – issues around the culture and competence of what went on at Murdoch-owned newspapers which have not been satisfactorily resolved or answered.”

Ed Miliband and Vince Cable have urged Karen Bradley, the culture secretary, to refer the takeover back to Ofcom. Photograph: Mark Thomas/Rex/Shutterstock

They add: “The Murdochs may claim that editorial independence could be guaranteed by ringfencing Sky news, and impartiality protected by Ofcom, the regulator. But the answer to this and the deeper questions at the heart of this bid depend on trust and the conduct of the Murdoch organisation and family does not inspire trust.

“If it was inappropriate for the Murdochs to take 100% control of Sky even before the multiple convictions of their former employees, it must be inappropriate now.

“Promises that might be made to the regulators that there will be a specified proportion of independent non-executive directors cannot overcome the reality of total ownership and control.”

Rupert Murdoch’s 21st Century Fox, which owns Fox News and a Hollywood studio, made a formal bid to take full control of Sky, owner of Sky News and pay-TV operations in the UK, Germany, Austria and Italy, on Thursday.