The government's review of its relationship with Oxfam comes amid fresh allegations in the paper that the charity failed to alert other aid agencies about the staff members' behaviour.
It is a "complete betrayal of both the people Oxfam were there to help and also the people that sent them there to do that job", Britain's global development secretary, Penny Mordaunt, told BBC News, which noted that the nonprofit received $44 million in government funds previous year.
It said an Oxfam report on the investigation stated there had been no allegations of abuse of beneficiaries and made no mention of any potential sexual crimes involving minors.
Responding to reports that staff who left Oxfam in Haiti later joined other aid agencies, without their knowledge of the incidents, Christian Aid said: "Christian Aid always follows robust recruitment procedures, such as securing references from legitimate sources, conducting Disclosure and Barring Services (DBS) checks where we are permitted to do so, and carrying out Counter Terrorism checks where required".
United Kingdom officials have said that Oxfam needs to hand over all its information on the issue in order to not lose funding.
She said her "absolute priority" was to keep the world's poorest and most vulnerable people safe from harm.
"Our approach to this matter would have been different had the full details that have been reported been disclosed to us at the time", the commission said.
Ms Mordaunt announced she would meet the charity on Monday to discuss the case, and said: "If the moral leadership at the top of the organisation is not there then we can not have you as a partner".
DfID said Oxfam had "serious questions" to answer following the revelations.
Speaking about the allegations, she said: "I think it's a complete betrayal of both the people Oxfam were there to help and also the people that sent them there to do that job".
If the moral leadership at the top of the organisation is not there then we can not have you as a partner.
"As a direct result of the stories in The Times, staff members have come forward with concerns about how staff were recruited and vetted in this case", said Caroline Thomson, chair of trustees for Oxfam GB.
"It is utterly despicable that sexual exploitation and abuse continues to exist in the aid sector", Mordaunt said in her overnight statement.
"The horrific behaviour by some members of Oxfam staff in Haiti in 2011 is an example of a wider issue on which DFID is already taking action, both at home and with the worldwide community via the United Nations".
Oxfam's chief executive has denied there was any cover-up after it was revealed some of its aid workers used prostitutes in Haiti in 2011.
Mordaunt spoke Sunday - three days after a Times of London investigation accused Oxfam's then-director in Haiti, along with other workers, of running an illegal makeshift brothel after a 2010 quake devastated the country.
The charity also said it had yet to find evidence proving allegations that underage girls were involved.