A soul-searching national inquiry into how authorities may have ignored systematic child abuse in some of Britain's most eminent institutions was launched by the home secretary.

Theresa May told the Commons she was establishing a powerful public inquiry into how complaints of sexual abuse were treated, and sometimes ignored, in public bodies over several decades.

Ministers had been holding out against such a sweeping inquiry, but, facing charges of an establishment cover-up, succumbed and promised there would be no no-go areas for the investigation.

The inquiry will be able to examine the files of the security services and allegations that the Tory whips' office in the 1970s may have suppressed allegations of child abuse by members of the parliamentary party. It is also expected to take some evidence from victims.

Labour MPs pointed to a 1985 BBC documentary in which a former government whip between 1970 and 1973 said that the Tory whips' office, when faced by an MP involved in "a scandal with small boys", would get him out of trouble, partly so the MP then felt obliged in the future to carry out the bidding of the whips.

May said she would look at plans, backed in principle by the Labour MP Tom Watson, to require public servants to report allegations of child abuse to officials in a form of mandatory whistleblowing. A duty to report would place some form of culpability on a public official if they knowingly withheld information concerning suspected child abuse.

Downing Street's haste to bow to the cross-party Westminster mood for a public reckoning was such that May, in her statement to MPs, was unable to name the chair of the expert panel that would lead the inquiry or its precise terms of reference. Separately, May said she had appointed Peter Wanless, chief executive of the National Society for the Prevention of Cruelty to Children (NSPCC), to examine how the Home Office last year reviewed allegations of child abuse by Westminster politicians between 1979 and 1999. Wanless will report within eight to 10 weeks.

However, while the broader public inquiry will produce an interim report before next year's election, the full report will not be completed until afterwards, May said.

A Home Office review last year found 114 potentially relevant files on child abuse were missing, destroyed or lost, but despite that May said last year's review found all credible evidence of child abuse had been passed to the prosecuting authorities.

May told MPs: "Our priority must be the prosecution of the people behind these disgusting crimes. That wherever possible – and consistent with the need to prosecute – we will adopt a presumption of maximum transparency. And that where there has been a failure to protect children from abuse, we will expose it and we will learn from it."

The flurry of activity follows many months of scandals involving celebrities and other figures in authority, but turned to Westminster at the weekend with claims that the former Conservative home secretary Lord Brittan had not properly handled potentially explosive allegations of child abuse by Westminster politicians brought to him in the 1980s by the late Tory MP Geoffrey Dickens.

Brittan came under further pressure after it emerged that he had been questioned by police in 1967 over reports that a woman had accused him of raping her. In a statementon Monday, Brittan said that allegation was "wholly without foundation" – and said he had correctly dealt with the material brought to him by Dickens.

The former Home Office minister David Mellor also sprang to Brittan's defence, writing in the Guardian: "Quite how this innocuous tale became the scandalous allegations and innuendos we have been hearing in recent days, beggars belief. There is no evidence whatsoever that Dickens was remotely dismayed by the way his dossier was treated, so why are so many other people anxious to be more Catholic than the Pope?"

Meanwhile a review by the Home Office has found that public money was given to two organisations linked to the Paedophile Information Exchange in the 1970s but the group itself was not directly funded by the taxpayer. May, the home secretary, ordered the investigation after a former employee claimed around £30,000 was given to PIE by the voluntary services unit of the Home Office.

Westminster, still suffering the reputational damage of the expenses scandal, dare not risk the charge of suppressing evidence of systematic child abuse by peers or MPs.

May said the wider panel inquiry, welcomed by most Westminster politicians, would have full access to papers and would, if necessary, at its request be upgraded to full public-inquiry status in line with the Inquiries Act, capable of requiring witnesses to give evidence.

There was a tension on Monday about the extent to which the inquiry will seek out new facts or instead more broadly draw out thematic lessons on how public authorities treated complaints of the child sexual abuse – partly drawing on the experience of cases of gang abuse in towns such as Rochdale and Oxford – and whether any gaps in child protection legislation still exist. General inquiries have either completed or are already underway into how bodies such as the BBC or hospitals failed to protect children.

May told MPs that the panel inquiry was not supposed to supplant existing police investigations saying: "I would expect the panel if they found allegations they believed were more appropriate for the police to investigate under a criminal investigation, for those allegations to be passed to the police." It would also have to consider whether calling a witness would in any way jeopardise or prejudice a criminal investigation taking place.Yvette Cooper, shadow home secretary, welcomed the government's decision and said the allegations "all at their heart have a similar problem – child victims weren't listened to, weren't heard, weren't protected and too many institutions let children down".