A confidential report by the charity said that there had been “a culture of impunity” among some staff in Haiti and concluded that children may have been among those sexually exploited by aid workers. The 2011 report stated: “It cannot be ruled out that any of the prostitutes were under-aged.”

Oxfam was part of a massive international relief effort in Haiti after the earthquake in Port-au-Prince in 2010, which killed 220,000 people, injured 300,000 and left 1.5 million homeless.

The revelations have caused international concern and triggered widespread coverage in the press throughout Europe. This morning Liz Truss, the chief secretary to the Treasury, called the revelations “shocking, sickening and depressing”.

Gavin Shuker, Labour MP for Luton South, said: “In case you were wondering, teenage girls, in one of the poorest countries in the world, immediately following an earthquake don’t by any measure ‘choose’ prostitution.”

One of the men allowed to resign without disciplinary action was Oxfam’s country director there, Roland van Hauwermeiren. The report said that Mr Van Hauwermeiren, 68, admitted using prostitutes at the villa rented for him by Oxfam with charitable funds.

Despite the admission, the charity’s chief executive at the time, Dame Barbara Stocking, offered the Belgian “a phased and dignified exit” because sacking him would have “potentially serious implications” for the charity’s work and reputation. After the internal inquiry, two other men in management were able to resign while four were dismissed for gross misconduct, including over the use of prostitutes at the apartment block where Oxfam housed them.

A number of sources with knowledge of the case said they had concerns that some of the prostitutes were under age. One said that men had invited groups of young prostitutes to their guesthouse and held sex “parties”. The source claimed to have seen footage from a night there that was “like a full-on Caligula orgy”, with girls wearing Oxfam T-shirts. The charity is understood to have no record of the footage being given to the investigation.

Prostitution is illegal in Haiti and the age of consent is 18. Paying for sex is against Oxfam’s staff code of conduct and in breach of United Nations statements on the behaviour of aid workers, which the charity supported. Oxfam said that it did not report any of the incidents to the Haitian authorities because “it was extremely unlikely that any action would be taken”. None of those accused has been arrested or faced any criminal charges.

The charity said that it disclosed the sexual misconduct to the Charity Commission but the regulator told The Times last night that it never received the final investigation report and Oxfam “did not detail the precise allegations, nor did it make any indication of potential sexual crimes involving minors”. The commission said that it was asking Oxfam to review what happened and “provide us with assurance that it has learnt lessons from past incidents and is taking all necessary steps to ensure risks are minimised”.

An appendix to the investigation report raised a lengthy list of management concerns over the situation in Haiti and asked: “How far back and why did the culture of impunity in Haiti develop . . . Were there signals that could have been picked up earlier?”

The charity acknowledged that staff in Haiti had felt intimidated and unable to raise the alarm. Sources with knowledge of the investigation alleged that the report had been “watered down” and one claimed that Oxfam bosses “deemed it unnecessary to pursue some of the allegations if we could get enough to simply dismiss the individuals”.

Oxfam announced in September 2011 that a small number of staff had left after a misconduct investigation. It stressed that the issues did not concern fraud over its £70 million aid budget in Haiti but did not disclose sexual misconduct. The charity said yesterday: “Oxfam treats any allegation of misconduct extremely seriously. As soon as we became aware of a range of allegations — including of sexual misconduct — in Haiti in 2011 we launched an internal investigation. The investigation was announced publicly and staff members were suspended pending the outcome.” It added that the allegations “that under-age girls may have been involved were not proven”.

Oxfam was founded by Quakers, social campaigners and academics in Oxford in 1942. It is Britain’s fifth largest charity, with an income of £392 million last year. Its British arm employs 5,300 people worldwide and works with 22,000 volunteers.