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Ashford MP Damian Green is "set to be cleared in days" after facing sleaze allegations.
It's claimed the frontbencher will not lose his job as First Secretary of State following claims pornography was found on his work computer.
In a separate allegation he has been accused of touching an activist's knee and making passes at her.
ITV's political editor Robert Peston said last night several Government sources have assured him that the job of the embattled minister is safe.
It follows allegations by an ex-Scotland Yard assistant commissioner that pornography was discovered on Mr Green's House of Commons computer during an investigation into Government leaks in 2008.
Mr Green has also been accused of inappropriate behaviour towards a political activist who claimed he had "fleetingly" touched her knee during a 2015 meeting in a London pub, and sent her a "suggestive" text two years later.
Mr Green, who is effectively the Prime Minister's deputy, has strenuously denied the allegations, calling them "untrue” and “deeply hurtful".
Robert Peston said: "I am told by three well-placed sources that Theresa May’s deputy, the First Secretary Damian Green, will be informed on Wednesday by the Cabinet Office and his boss that he does not need to resign.
"According to several members of the Government, no other women have presented evidence against Mr Green.
"And the police testimony does not prove beyond all doubt that it was Mr Green himself who was watching the porn on the parliamentary equipment - which should not have been used in this way."
Mr Green has been under investigation for several weeks on whether he has breached the ministerial code.