Number 10 refuses to say when report will conclude or if findings will be published

Theresa May faced a storm of criticism from senior MPs last night over her government’s handling of an inquiry into alleged inappropriate behaviour by her deputy, Damian Green, after Downing Street suggested a report into his conduct might never be published.

Green, the first secretary of state and de facto deputy prime minister, is under investigation by the Cabinet Office over claims he made inappropriate advances to a young Tory party activist and that pornography was found by police on his House of Commons computer.

Green has strenuously denied both sets of claims.

Last night, however, Downing Street refused to say either when the inquiry would be concluded or whether the results would be made public, prompting claims that May was going back on a previous commitment to full transparency.

The Liberal Democrat leader Sir Vince Cable called for the report to be published as soon as possible, both in the interests of openness and to lift the cloud of suspicion over May’s closest ally in government. It was also vital that the public knew who would step in at times when May was out of the country or away from Number 10 for other reasons.

Cable said: “Governments need deputy prime ministers, particularly governments that are embattled, as this one is over Brexit. Damian Green has brought some much-needed moderation to this government, but it is difficult for him to carry on his duties as deputy in all but name with this hanging over him. The report needs to be published as a matter of urgency. The public are entitled to know who is running the country in the absence of the prime minister, and that person must do that without an investigation hanging over their head.”

The Labour MP Lucy Powell added: “Full disclosure and transparency is absolutely key in these cases. The government is only going to get itself in more hot water if it refuses to publish this report.

“Damian Green is the second most powerful politician in the country. That person needs to be beyond suspicion but doubts will remain unless they are completely open and honest.”

A Labour shadow cabinet source went further, saying that if the report was kept under lock and key it would invite inevitable charges that the prime minister was protecting her favourite and most powerful minister. “If this is not published, the suspicion will be that there is a cover-up – and one ordered by the prime minister.”

As well as being a friend of May’s over four decades, Green is comfortably the most powerful minister serving under her. He sits on around 20 cabinet committees, most of which he chairs. He is also a key player in helping to determine Brexit strategy.

Recently, Green announced plans for a green paper into one of the most urgent issues facing the government – the future of social care and the challenges of providing for an ageing population.

Having already lost two cabinet ministers in the past month – defence secretary Michael Fallon and international development secretary Priti Patel – May will be desperately hoping that she does not have to sacrifice Green and hold another reshuffle.

The Cabinet Office inquiry is being run by its head of propriety and ethics, Sue Gray. It was launched in early November, after the Conservative activist Kate Maltby wrote a piece in the Times claiming Green had touched her knee in 2015 and, one year later, sent her a suggestive message.

As a tide of allegations about the behaviour of MPs then swept Westminster, allegations also surfaced that pornography of an “extreme” nature had been found on Green’s computer after a police raid in 2008. Green insisted he had never been informed by the police that any such material had been found at the time and denied the claims, as well as those made by Kate Maltby.

The Labour MP Jess Phillips said the main recommendations and findings of the report should be made public “for the sake of transparency”, though all the detail need not be. She added: “The political class must show it is taking this seriously and learning lessons. Lots of politicians are running to protect themselves, rather than trying to change the culture.”