A seventh inquiry into lobbying has been set up, as Downing Street refused to say when an investigation into senior civil servants’ second jobs would be made public. On Friday the National Audit Office (NAO) became the latest organisation to launch an inquiry into the relationship between the finance firm Greensill Capital and government figures. It followed revelations that began with the former prime minister David Cameron lobbying on behalf of the businessman Lex Greensill and have snowballed to engulf mandarins and politicians across Westminster. After it emerged on Tuesday that Greensill had hired a civil servant who continued to work in Whitehall, Simon Case, the cabinet secretary, told colleagues they should make sure all outside interests were declared by the end of this week. On Friday, Boris Johnson’s deputy spokesman promised the results of Case’s investigation would be provided to the public inquiry launched by the government and led by Nigel Boardman, a corporate lawyer. But the spokesman refused to say when the findings would be made public, and whether they would be published in full. “I’m obviously not in a position now to set out the exact details of how and when it will be published,” he said in a briefing with journalists on Friday. The prime minister’s spokesman promised Boardman would get “maximum possible access to all the information he needs”. He also confirmed the prime minister had “full confidence” in Matt Hancock, insisting the health secretary had “acted entirely properly” in declaring his interests in a family firm that reportedly won contracts from the NHS. Becoming the latest organisation to launch an inquiry, the NAO said the British Business Bank had been acting as an administrator on behalf of the government for the coronavirus financial support scheme for large businesses, and authorised Greensill Capital to issue financial support in June 2020, before the firm filed for insolvency last month. The inquiry would cover “Greensill Capital’s involvement in the government’s Covid-19 support schemes, including the accreditation process, and any post-accreditation monitoring of Greensill Capital’s activities”, the NAO said. Labour welcomed the move, saying it should “get to the truth about why hundreds of millions of pounds of taxpayer money were put at risk by the decision to accredit Greensill Capital to the CLBILS Covid loan scheme”. Bridget Phillipson, the shadow chief secretary to the Treasury, added: “There are other urgent questions. We would also welcome an investigation into why government entered into supply chain finance contracts with Greensill Capital, and to what degree that delivered value for money for the taxpayer.” Other investigations already launched into the scandal concerning Greensill include ones by three select committees – including two led by Conservative MPs – and the Committee on Standards in Public Life, which is chaired by the former MI5 director general Jonathan Evans. Cabinet ministers such as Hancock and the chancellor, Rishi Sunak, are likely to be asked to give public evidence to the inquiries. Johnson urged people to wait for the public inquiry into Greensill to conclude, saying on Thursday: “I think the most important thing is for us to get to the bottom of it properly. I want all ministers and civil servants to be making the information that needs to be known, known to Mr Boardman and let’s see what he has to say. We need to understand completely what’s gone here.”