Among the alleged misconduct is paying sex workers and sexual abuse.
Britain's global development secretary Penny Mordaunt told the aid agency to front up tomorrow in London to explain why it appeared to cover up a sex scandal.
"With regard to Oxfam and any other organisation that has safeguarding issues, we expect them to co-operate fully with such authorities, and we will cease to fund any organisation that does not".
He added: "If we can be part of helping with references or cross-checking then we'll play an active part in that because I've seen the unbelievable work that Oxfam is doing in the Congo, Syria, in Bangladesh, Yemen, in places other people simply won't go".
But the former minister Priti Patel said she was not surprised.
Despite the claims arising publicly on Friday, Ms Patel said "a lot of people knew about this".
"What I'm apologising for is that nine Oxfam staff behaved in a way that was totally unacceptable and contrary to our values, and that led much more responsible staff to make decisions which are now seen by some as being marginal or inappropriate".
She added she was writing to all United Kingdom charities which receive United Kingdom aid asking them to spell out the steps they are taking to ensure safeguarding policies are in place and working properly. The agency, which gave £31.7 million ($55.2 million Cdn) to Oxfam a year ago, demanded that Oxfam's senior officials meet with it to explain their actions.
Professor Andrew MacLeod, from Hear their Cries Charity, was damning of how organisations dealt with claims.
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".
"The problem is this, you have a lot of white men in positions of power with a lot of wealth going to underprivileged countries where the rule of law has broken down and abuse takes place".
But Professor MacLeod said cutting funding was not the answer.
Caroline Thompson, who chairs Oxfam Great Britain's board of trustees, said charities that work in "fragile and unstable environments can become targets for abusers", but that the organization is committed to fixing the problems it faces.