The NAO said the investigation would examine the circumstances surrounding the closure of the charity, which was funded by the Home Office to offer support to people who had experienced domestic violence in same-sex relationships.
In a statement announcing the investigation, the NAO said it would be looking into the role of the Charity Commission and other public sector bodies as well as the financial management of the charity, Home Office oversight and the clarity of grant agreements.
After Broken Rainbow closed in June, the news website BuzzFeed reported that it had seen a cache of documents that showed grants worth tens of thousands of pounds from funders such as the Home Office and Comic Relief were spent within 24 hours of receipt, often on basic running costs.
It added that £23,000, which it said was enough to run the charity’s helpline for six months, had been spent on travel expenses, mainly for the charity’s chief executive, including £800 on one train ticket. BuzzFeed claimed a treasurer had quit weeks after being appointed, warning that restricted funds might have been spent illegally.
The Charity Commission opened a case about the charity in September 2015. A spokesman said: "The commission has an open case into the charity that is ongoing and it is liaising closely with the Insolvency Practitioner."
He said it was also working with the NAO and assisting with its inquiry into the funding of the charity.
The investigation comes after a letter to the NAO from Bernard Jenkin, chair of the Public Administration and Constitutional Affairs Committee, came into the public domain. The Conservative MP for Harwich and North Essex wrote to the NAO in July asking it to look at the charity.
In the letter, Jenkin said some were referring to the charity as "the new Kids Company" and suggested that the NAO should look into the arrangements the Home Office made to control its expenditure on the charity.
He wrote that it would be very useful to the committee and to the public to know what had happened, how far the lessons had been absorbed and whether the Home Office had any contingency plans.
The NAO’s investigation is due to conclude next spring and it has called on anyone who wants to speak to the investigation team to email email@example.com.