The allegations have been most prominently promoted by the 'Guido Fawkes' blog. Its author Paul Staines earlier responded to criticism, from Iain Dale on the right as well as this blog on the left, of his increasingly single-issue blog by tweeting a tribute to controversial ex-Sun editor Kelvin MacKenzie, whom he regards as a moral compass:
We solve all the blog's ethical dilemmas by asking ourselves "what would Kelvin MacKenzie have done?"
Which is funny - because Kelvin might well join those telling Guido to put a sock in it.
Or rather, Guido may be relying on Old Kelvin, not New Kelvin. Old Kelvin said of his target 1980s readership, according to the 'Stick it up your junta' unauthorised history his Sun years.
"You just don't understand the readers, do you, eh? He's the bloke you see in the pub, a right old fascist, wants to send the wogs back, buy his poxy council house, he's afraid of the unions, afraid of the Russians, hates the queers and the weirdos and drug dealers. He doesn't want to hear about that stuff [serious news]".
By 2003, Mackenzie was more than ready to move on, saying he had become "vaguely more liberal": "All that old 'pulpit poofs' stuff was 15 bloody years ago ... I'm just older now and I've moved on"
By this year, New Kelvin could be found waxing lyrical on the Today programme about how anti-discrimination laws "had made a dramatic and welcome difference" in changing the public culture in a more liberal Britain - so that the readers "couldn't give a damn" about somebody's sexuality.
It was 12 years ago - right back in 1998 - that The Sun, then edited by David Yelland - announced something of a change of mind, just days after being criticised for its front-page splash "Are we being run by a Gay Mafia", as the BBC reported at the time.
The paper's editor, David Yelland, said that in future, the paper would not "out" gay people unless it was in the public interest.
"We will continue to be in the vanguard of this debate - and all debates - but we will not invade the privacy of gay people by outing them."
Mr Yelland added: "The Sun is no longer in the business of destroying closet gays' lives by 'exposing' them as homosexuals.
William Hague is quite clear that the allegations are untrue and malicious. Perhaps Guido should give Kelvin a call about how he might respond.