The accusation relates to his time with Save The Children in the year before his wife was killed by a far-right fanatic during the 2016 Brexit referendum campaign.
It is claimed that Mr Cox drunkenly harassed a female employee at the charity in London, forcing her against a wall outside a bar, holding her by the throat and telling her: "I want to f*** you."
The incident led to him being forced to leave the charity in 2015. Save The Children's chief executive Justin Forsyth, a close friend of Mr Cox and former aide to Labour Prime Minister Gordon Brown, resigned four months later.
Astonishingly, one month after Mr Cox left the charity, a senior female US Government official told police Mr Cox had carried out a similar alleged assault on her at Harvard University in America – as this newspaper revealed last week. The woman was unaware of the Save The Children incident at the time.
In another development, it emerged yesterday that Mr Forsyth was also the subject of a complaint by a female employee. It related to an "inappropriate comment" he allegedly made. The complaint was investigated and said to have been resolved "by consensus".
Insiders insist Mr Forsyth's subsequent departure from the charity had nothing to do with the complaint against him, nor the handling of the Cox scandal. Mr Forsyth was then appointed deputy executive director of Unicef in New York, a post he still holds.
A Save The Children source said: "Brendan and Justin were a formidable double act. But they were too big for their boots."
The disclosures will fuel the current controversy over charity sex scandals and cover-ups.
Mr Cox said in a statement to this newspaper: "I accept I have made mistakes, behaved badly and caused some women hurt and offence. I take responsibility for what I have done. I apologise unreservedly for my past behaviour and am committed to holding myself to much higher standards of personal conduct in the future."
It marks a dramatic fall from grace for Mr Cox, who has won praise for the way he has focused on bringing up his and his wife's two young children and thrown himself into charitable work since her death.
He says he is determined to end his "deeply inappropriate" behaviour and strive harder to keep the vow he made after his wife's murder to "love and protect our children and fight the hatred that killed Jo".
But Mr Cox said the furore over his conduct made his charity work more difficult and he would therefore give up public life – for now at least.
Brendan and Jo met while working for Oxfam, where Mr Forsyth had been their boss. Mr Forsyth became Gordon Brown's campaigns chief when he became Prime Minister in 2007, and Mr Cox joined him in Downing Street, while Mrs Cox became an adviser to Sarah Brown. The Coxes married in 2009.
When Labour lost the 2010 Election, Mrs Cox followed her political dream – eventually being elected MP in 2015. Mr Forsyth became Save The Children's chief executive and Mr Cox went with him as director of policy, including responsibility for the "empowerment of women."
Some colleagues say he had a reputation for pestering women for sex. "It wasn't comfortable being on duty alone with him," said one.
"He would buy women drinks, his hands were everywhere. Everyone knew it was going on, but he was best friends with the boss."
Matters came to a head after a Save The Children drinks party in July 2015. "Brendan was dancing provocatively with a woman who told him to leave her alone," said one source.
"She joined a group of women who went on to a bar. Brendan followed them. He got her outside, pushed her against a wall and tried to force himself on her."
Another source said: "He was drunk, said, "I want to f*** you" and held her by the throat. She was outraged and made a complaint."
Some female employees are said to have feared Mr Cox was "shielded" by Mr Forsyth, and threatened to resign unless Mr Cox was fired.
Charity chiefs suspended Mr Cox, banned him from the office and set up a disciplinary panel. Mr Forsyth did not sit on the panel because of their close friendship.
But the investigation was effectively scuppered when Mr Cox refused to attend a disciplinary hearing and suddenly resigned. The charity was told they could not find him guilty of misconduct without hearing his side of the story.
The ploy also meant Save The Children could not tell Harvard he had been found guilty of misconduct when he attended a course there four weeks later. This newspaper revealed last week how a woman, whose identity we withheld, complained to US police, accusing Mr Cox of sexual assault while there.
By her account, he cornered her in a bar, plied her with drink, "grabbed her by the hips, pulled her hair, forced his thumb into her mouth in a sexual way" and later sent her obscene text messages. Police filed her complaint as "assault and battery", but she told them not to take further action because she "feared repercussions".
Mr Cox last week called the allegations "spurious". Yesterday he said he did not "recognise or accept" her claims.
Following the murder of his wife, there were reports that Mr Cox was lined up to succeed her Labour MP for Batley and Spen in Yorkshire, but he did not do so. The Mail on Sunday has been told Labour officials advised against it because of rumours about his behaviour.
Mr Forsyth's successor as Save The Children chief executive, Kevin Watkins, last night announced new measures to stop staff being abused by colleagues in the wake of the allegations about Mr Cox.
He pledged to take charge of a major shake-up of the charity's complaints procedure and vowed a "zero tolerance of disrespectful behaviour".
Mr Watkins could face tough questions over the Cox scandal – as well as other allegations of misconduct by aid workers – when he is quizzed by MPs this week.
Mr Forsyth declined to comment last night.
