'They would invite women for parties, we knew they weren't just friends but something else, ' said an anonymous former employee.
The charity should immediately hand over its entire 2011 investigation into the sexual misconduct to the appropriate prosecuting authorities and the Charity Commission, she said.
Penny Mordaunt condemned the behaviour of some Oxfam staff members as a "complete betrayal", as she warned the charity the "scandal" had put its relationship with the Government at risk.
Oxfam said it now had a dedicated safeguarding team, a confidential whistleblowing hotline and safeguarding contact point within countries, and a code of conduct that stipulated: "I will also not exchange money, offers of employment, employment, goods or services for sex or sexual favours".
Oxfam says it investigated the allegations in 2011.
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The apology comes as the Department of worldwide development, which previous year gave Oxfam more than £30 million, said it will review whether or not to continue to fund the charity.
Oxfam has denied any cover-up and has said the behaviour of some of its staff in Haiti had been "totally unacceptable".
"I am deeply ashamed about Oxfam's behaviour then", CEO Mark Goldring told ITV News.
He added: 'Everybody - the 25,000 staff and volunteers - are compromised by this, the hundreds of thousands of people who support Oxfam every month are compromised by this, and to everybody I apologise.
"But I don't think it was in anyone's best interest to be describing the details of the behaviour in a way that was actually going to draw extreme attention to it".
"I have so much respect for Oxfam, they do great work, but this is a sector-wide problem".
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Ms Mordaunt told BBC1's The Andrew Marr Show that the failure to pass on information to relevant authorities shows an "absolute absence of leadership".
"Our approach to this matter would have been different had the full details that have been reported been disclosed to us at the time", it said in a statement.
Ms Mordaunt said she had written to all United Kingdom charities that receive aid from the Government and asked them to explain the measures they took to implement safeguarding measures.
Ms Mordaunt said the charity had also "categorically" stated to the Department for International Development (DfID) that no harm was done and beneficiaries were not involved. Asked if that was a lie, Mordaunt said: "Well, quite".
But Ms Mordaunt said it was "shocking" some staff had been able to resign after the Haiti sex allegations surfaced.
Individuals closely implicated in the scandal went on to take leadership roles in other charities, which were not informed of the reasons they left Oxfam and even given glowing references, the investigation added.
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"I am writing to all United Kingdom charities which receive United Kingdom aid, insisting that they spell out the steps they are taking to ensure their safeguarding policies are fully in place and work properly, declare all safeguarding concerns they are aware of, and confirm they have referred all concerns they have about specific cases and individuals to the relevant authorities", she said.
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