Oxfam’s deputy chief executive has resigned over the prostitution scandal engulfing the charity, saying she is “ashamed” of what happened.

Penny Lawrence said she took “full responsibility” for the behaviour of the charity’s staff in Chad and Haiti “that we failed to adequately act upon”. She said she was sorry for the “harm and distress” it had caused supporters.

The announcement comes after talks between Oxfam bosses and ministers yesterday and amid continuing criticism of the charity’s response to the allegations. The Times reported last week that senior aid workers had used prostitutes in Haiti during the relief effort after the devastating earthquake in 2010, something which is illegal.

An internal investigation by the charity into sexual exploitation, the downloading of pornography, bullying and intimidation is claimed to have found children may have been exploited by employees.

Oxfam has since faced further allegations that prostitutes were also used by staff in Chad in 2006. The claims continued yesterday, with allegations the charity was aware of concerns about the conduct of two of men at the centre of the Haiti allegations when they previously worked in Chad.

Oxfam has denied trying to cover up the use of prostitutes by staff in Haiti and has announced measures to try to improve safeguarding at the charity.

In a statement, Ms Lawrence said: “Over the last few days we have become aware that concerns were raised about the behaviour of staff in Chad, as well as Haiti, that we failed to adequately act upon.

“It is now clear that these allegations involving the use of prostitutes and which related to behaviour of both the Country Director and members of his team in Chad were raised before he moved to Haiti.

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“As programme director at the time, I am ashamed that this happened on my watch and I take full responsibility. I am desperately sorry for the harm and distress that this has caused to Oxfam’s supporters, the wider development sector and most of all the vulnerable people who trusted us.”

International Development Secretary Penny Mordaunt said the charity had lied and failed in its “moral leadership” by not fully disclosing details of its investigation to the relevant authorities.

She called the behaviour “utterly despicable” and threatened to cut the charity off from Government funding if she was unsatisfied with the answers from Monday’s meeting.

The Charity Commission has also said it was not told the full story when Oxfam first looked into the allegations in 2011. Four members of staff were dismissed and three, including the country director Roland van Hauwermeiren, resigned before the end of the probe.

Ms Mordaunt’s predecessor told Sky News that senior officials had “pushed back” against an inquiry into alleged abuse.  Priti Patel said “a lot of people knew about this”, and added in a Daily Telegraph article that the Oxfam claims are “only the tip of the iceberg”.

Ms Mordaunt has defended her department, saying she first heard about the claims when they were made in The Times. Following Ms Patel’s claims, Downing Street refused to say if the Prime Minister retained full confidence in senior officials at the Department of International Development (DfID).

When asked, a Number 10 spokesman said: “The Prime Minister, of course, has full confidence in the Secretary of State to lead this department, a department which has already taken action on this issue.”