It came as Development Secretary Penny Mordaunt claimed sex predators were targeting aid organisations because of the chaotic environments in which they work.
Save the Children said it investigated 31 cases of sexual harassment last year, which resulted in 16 people being fired and 10 being referred to police or other authorities.
The charity added that none of the cases involved children and all of them occurred abroad.
The British Red Cross there were a “small number” of sexual harassment cases last year in the UK and “appropriate (action) was taken”.
Christian Aid said it investigated two sexual misconduct cases in the last year, which led to it sacking one worker and carrying out disciplinary action against another.
The revelations followed a report in The Sunday Times that more than 120 British charity workers were accused of sexual abuse last year.
Oxfam, which was attacked for its handling of allegations that some of the charity’s staff in Haiti arranged sex parties with prostitutes after the 2010 earthquake, continued to be the subject of scrutiny.
Ms Mordaunt said the charity “completely failed to do the right thing” and warned Oxfam it faced losing all its Government funding if it did not show “moral leadership”.
The Department for International Development (DFID) gave Oxfam £31.7m last year.
Ahead of a meeting on Monday with Oxfam officials to discuss the scandal, she told the BBC’s Andrew Marr programme: “If they do not hand over all the information they have from their investigation and subsequently to the relevant authorities… then I cannot work with them anymore as an aid delivery partner.”
Ms Mordaunt said the charity had done “absolutely the wrong thing” by failing to tell the Charity Commission and prosecuting authorities the full details of the allegations.
Oxfam said it has dismissed four people and allowed three others to resign after an internal 2011 investigation.
It said allegations that staff members had sex with minors were “not proven”.
Caroline Thomson, chair of Oxfam’s trustees, announced a package of measures to show the organisation was committed to changing.
She said it had made “big changes” since the original incident but that “today I commit that we will improve further”.
Ms Mordaunt has written to all UK charities which receive UK aid to tell them they must declare all “safeguarding concerns” or lose Government funding.
It came amid an explosive intervention by her predecessor, Priti Patel, who claimed she faced “internal pushback” when trying to investigate exploitation claims against aid workers.
“A lot of people knew about this,” she told Sky News, naming the Charity Commission and DFID.
“I did my own research and I have to say I had a lot of pushback within my own department.
“I pushed hard – I had pushback internally and that is the scandal. The scandal is within the industry, people know about this.”
A statement from DFID responding to the allegation said the Haiti incident was “an example of a wider issue on which DFID is already taking action, both at home and with the international community via the UN”.
The Charity Commission said it had written to Oxfam “as a matter of urgency” to request further information and “establish greater clarity”.
The executive director of Oxfam International said on Sunday she was heartbroken by the scandal.
Winnie Byanyima said: “I feel deeply, deeply hurt. … What happened in Haiti was a few privileged men abusing the very people they were supposed to protect – using the power they had from Oxfam to abuse powerless women. It breaks my heart.”