Emma Harrison has denied any wrongdoing

Ministers are facing fresh questions as to how welfare-to-work entrepreneur Emma Harrison came to be appointed David Cameron's "family champion" just a month after officials were notified of allegations of fraud at her company.

Shadow work and pensions secretary Liam Byrne said that with hundreds of millions of pounds of public money at stake, the government's handling of the case went to the heart of its judgment.

In a letter to Work and Pensions Secretary Iain Duncan Smith, he called on him to say when ministers in his department were informed of the fraud allegations and when No 10 was told.

Last week Harrison announced she was quitting as an unpaid Downing Street adviser and as chairman of A4e, which won millions of pounds worth of contracts from the government's Work Programme, saying she did not want to be a "distraction".

Earlier in the week, A4e issued a statement saying it had uncovered the alleged fraud, relating to four employees who have since left the company, in November 2010 though its internal systems. It said it notified officials at the Department of Work and Pensions within 48 hours of the discovery.

The following month, on December 10, Cameron announced he was appointing Harrison as his adviser on dealing with troubled families.

The fraud allegations are currently under investigation by Thames Valley Police who last month arrested four people in relation to the case.

In his letter to Duncan Smith, Byrne said: "Given that your department knew about the allegations, they go to the issue of the government's judgment in how it dealt with them.

"Given your department's close relationship with A4e and Emma Harrison, what role did you play in her appointment as the government's troubled families adviser?

"Were these allegations discussed during the appointment process of Emma Harrison, and, if not, why not?"

A spokeswoman for the DWP said that they could not discuss allegations relating to an ongoing police inquiry.

"We have been clear that if there is any evidence of systematic fraud at A4e relating to previous or current business we will terminate existing contracts," the spokeswoman said.