Theresa May, the home secretary, has been accused of delaying the release of a completed report about the Home Office’s handling of child abuse allegations during the furore about who should chair the new official inquiry into what happened.

May is under growing pressure because of the way she has overseen the setting up of the inquiry. On Friday, Fiona Woolf became the second senior legal figure to resign as chair owing to concerns about her connections to the Westminster establishment.

It has now emerged that May was sent a separate review on 15 October by the NSPCC chief, Peter Wanless, who was tasked with looking into the way the Home Office dealt with an investigation into child abuse allegations between 1979 and 1999.

But the department is refusing to make that review public at this stage, with a spokesman saying there is no specific date yet for its release as May is still considering the “substantial” document.

Wanless said he wanted the report to published as soon as possible, when asked by the Guardian on Sunday night, but added: “It was requested by the home secretary so it is for her to decide on when to publish and explain timing.”

May is scheduled on Monday to answer questions from MPs on the inquiry – which has been branded “chaotic” by Keith Vaz, the Labour chairman of the home affairs committee.

Victims’ groups, who are calling for a tougher judge-led inquiry with more powers to compel witnesses to give evidence, have been frustrated about being shut out of the process.

On Sunday, Yvette Cooper, the shadow home secretary, called for the Wanless review to be published, saying there are “widespread issues around child abuse that takes place in the home but also the way institutions respond to that … whether they respond in the right way to it”.

That the report has been completed emerged in a parliamentary answer given by John Mann, a Labour backbencher who has campaigned on the issue.

Norman Baker, a Home Office minister, told MPs: “The review has had access to all material identified which would relate to child abuse and which the department still holds. The home secretary has now received the report of the review and is considering its findings ahead of the full report being published.”

Mann told the Guardian there was “no reason why it should not be published” and that he would be pressing May about it in the Commons on Monday. However, he warned that the report probably raised more questions than it answered as the team did not have access to documents protected by the Official Secrets Act.

Woolf resigned as chair of the inquiry on Friday because of her friendship with a neighbour, Lord Brittan. The former Tory home secretary is under scrutiny because a dossier containing accusations about Westminster paedophile activity went missing from his department during the 1980s. He denies any failure to act and there is a letter suggesting it should have been passed on to police.

• This article was amended on 3 November 2014. An earlier version stated that Norman Baker would press Theresa May in the Commons on Monday about the report. In fact it is John Mann who will raise the issue.