Prime Minister David Cameron has said there will be "no stone unturned" by an independent inquiry into how public institutions handled allegations of child abuse, declaring it was "vital" to find out the truth of what happened and to learn lessons.

Home Secretary Theresa May is expected to announce a broad independent inquiry later today as she makes a statement to MPs about claims of organised child abuse at Westminster in the 1980s.

Conservative peer Lord Brittan has welcomed the probe, but insisted that claims he failed to deal adequately as home secretary with a dossier of information handed to him by campaigning MP Geoffrey Dickens in 1983 were "completely without foundation".

Demands for an inquiry were fuelled over the weekend by Lord Tebbit, a member of Margaret Thatcher's cabinet in the 1980s, who said that there "may well" have been a political cover-up at the time in order to protect "the system".

Speaking during a visit to Halesowen College in the West Midlands, Mr Cameron said: "I am absolutely determined that we are going to get to the bottom of these allegations and we're going to leave no stone unturned to find out the truth about what happened - that is vital.

"It is also vital we learn the lessons right across the board from these things that have gone wrong.

"And it's also important that the police feel that they can go wherever the evidence leads and they can make all the appropriate arrangements to investigate these things properly.

"Those three things need to happen - robust inquiries that get to the truth, police investigations that pursue the guilty and find out what has happened and proper lessons learned so we make sure these things will not happen again.

"That is what will happen under my Government."

Following a review last year, the Home Office admitted that more than 100 files relating to allegations of child abuse have gone missing over a period of 20 years. They included a dossier, alleging the involvement of public figures in a paedophile ring, handed to then home secretary Leon Brittan by Mr Dickens, who died in 1995.

The missing dossier is believed to be linked to the alleged abuse of children at the Elm Guest House in south-west London.

In a statement today, Lord Brittan said: "I would like to put on record that I welcome the fact that there is now to be an independent review to look at the missing files belonging to the Home Office.

"It has been alleged that when I was Home Secretary I failed to deal adequately with the bundle of papers containing allegations of serious sexual impropriety that I received from the late Geoff Dickens MP. This... is completely without foundation - as evidence from the Home Office's own report supports.

"As I made clear in the statement that I issued on 2 July, I passed this bundle of papers to the relevant Home Office officials for examination, as was the normal and correct practice. I wrote to Mr Dickens on 20 March 1984 informing him of the conclusions of the Director of Public Prosecutions about these matters (as set out in the Interim Report of the Independent Review set up by the Home Office).

"In this same report, Mr Dickens thanked the Home Office for the way in which the information he provided was handled and said in a speech to the House of Commons on 31 March 1987: ' I should like to place on record my thanks to the Home Office and the departments within the Home Office for following up the cases that I keep sending to it. I should also like to thank the Attorney General. They have been very helpful and a strength to me in my campaigns.'"

Downing Street said there would be an emphasis on speed when the inquiry is set up but sidestepped questions over whether it would report back before the general election in May 2015.

The Prime Minister's official spokesman said: "We want to make sure that answers are achieved as quickly as possible. Clearly it needs to be a process that commands confidence and credibility as well."

Mr Cameron has taken a "close personal and detailed interest" in the claims being made and had held "extensive discussions" with his team over the weekend.

The spokesman said that the Prime Minister has not discussed the claims being made with Lord Brittan.

Meanwhile, Lord Brittan also confirmed that he had been interviewed by police in relation to a separate "serious allegation", which is not believed to be linked in any way to the child abuse claims. He said that the allegation against him was "wholly without foundation".

The 74-year-old Conservative peer's statement came after reports that he had been questioned under caution in connection with a historic rape allegation.

The Metropolitan Police have confirmed that officers received an allegation in 2012 from a woman who claimed she was raped by a man at a London address in 1967, when she was aged over 18. The allegation is being investigated by officers from the Sexual Offences, Exploitation and Child Abuse Command.

Scotland Yard said: "In June 2014, a man aged in his 70s was interviewed under caution by appointment at a central London location in connection with the allegation. He was not arrested. Inquiries continue."

Lord Brittan said: "It is true that I have been questioned by the police about a serious allegation made against me. This allegation is wholly without foundation."

Asked about Mrs May's statement to MPs this afternoon, a Home Office spokesman said: "It is right that the detail of her statement should wait until she speaks in the House of Commons, but her statement will address the two key public concerns.

"First, the Home Office's response in the 1980s to papers containing allegations of child abuse.

"And second, the wider issue of whether public bodies and other institutions have taken seriously their duty of care towards children."

The inquiry - which could involve a panel of experts taking evidence from the public - is expected to take place alongside a QC-led review of the Home Office's failure to keep hold of documents alleging organised abuse.

The permanent secretary at the Home Office, Mark Sedwill, has said he will appoint a senior legal figure - following the intervention of Mr Cameron - to conduct a fresh inquiry in order to establish whether the findings of the previous review remained "sound".

Over the weekend, he disclosed that last year's review had identified 114 potentially relevant files from the period 1979 to 1999, which could not be located and were "presumed destroyed, missing or not found".

The earlier review - conducted by an HM Revenue and Customs investigator - concluded the relevant information in the Dickens file had been passed to the police and the rest of the material destroyed in line with departmental policy at the time.

It was reported today that police have traced an alleged victim who has "implicated a senior political figure" in abuse at the Elm Guest House.

The man, who is now in his 40s and based in the US, has given a detailed account of how he was assaulted by the politician, but has so far refused to make a formal statement to detectives, said The Daily Telegraph.

The Home Office is also facing claims that a leading member of the notorious Paedophile Information Exchange (PIE) used its premises to store material.

Steven Adrian Smith had clearance to work as an electrical contractor at the Westminster building in the late 1970s and early 1980s when he chaired PIE.

According to the BBC, in a 1986 book available in a restricted part of the British Library, he wrote: "I had a furnished office completely to myself seven days a week on a rotating shift basis.

"Much of PIE's less sensitive file material was stored in locked cabinets there, where no police raid would ever have found them."

Labour's shadow home secretary Yvette Cooper accused the Home Office of failing to respond to legitimate public concerns.

"The Government must take these concerns extremely seriously - to make sure justice is done for victims of abuse no matter how long ago, to make sure that any institutional failure is uncovered, and to make sure that lessons are learnt and that child protection is as effective as possible for the future," she said.

"We need a wide-ranging review that can look at how all the allegations put to the Home Office in the 80s and 90s were handled. Any stones left unturned will leave concerns of institutional malaise, or worse a cover-up, unaddressed."

Concerns about a child abuse ring with links to Westminster were raised in Parliament in 2012 by Labour MP Tom Watson. The current pressure for a new inquiry was sparked by evidence given to the House of Commons Home Affairs Committee earlier this month by another MP, Simon Danczuk, who urged Lord Brittan to reveal what he knew about the Dickens file.

The Committee's chairman Keith Vaz said any inquiry must be independent of Parliament.

Mr Vaz told BBC Radio 4's World At One: "I don't think Parliament should be conducting inquiries. This is not the role of the Home Affairs Select Committee.

"We came to a stage on phone hacking where we thought the evidence was so huge and the neglect so great that it really had to go outside Parliament. We have reached that stage at the moment, not because people can't be trusted to conduct the inquiry, but (because) we don't have the expertise and the ability to do it.

"This must go outside Whitehall, it must go outside Westminster to independent figures, who can examine what Simon Danczuk, Tom Watson and others have said."

Mr Watson told World At One: "The one thing I think this inquiry needs is the power to oblige organisations to reveal documents - the kind of inquiry that can go where the intelligence leads it, I think, is important."

He added: "There are too many incidents of inquiries being closed down or not opened up or not adequately resourced or information going missing or survivors claiming they were too scared to speak out or they were leaned on for me not to be concerned that there may have been historic cover-ups.

"That's why I think this inquiry should have the powers to go where those allegations and where the intelligence leads them. We just don't know what went on in the 70s, 80s and 90s and without the right powers we are never going to know.

"I think a Hillsborough-style inquiry where the panel are allowed to form a view without prejudicing potential criminal trials is probably quite useful, so not taking evidence under oath might be an advantage.

"But in this particular inquiry, the power to seize documents from agencies like Special Branch or some of the other agencies of the state or other police authorities will be vital if we are going to get to the facts."

Mr Danczuk yesterday said he had been approached ahead of the Home Affairs Committee hearing by Mr Vaz, who told him that some members of the cross-party committee were concerned that he might be planning to use parliamentary privilege to name individuals in connection with the abuse allegations.

The committee chairman told World At One: "I always speak to MPs who are called to give evidence to the committee... to remind them of the issues of privilege and to tell them how the session will be going."

Mr Vaz declined to reveal whether committee members had voiced concerns to him about what Mr Danczuk might say, but added: "People have conversations with me at all times, including members of the press, about select committee hearings, but at the end of the day it's up to the witnesses themselves to come before the committee.

"No witness before the select committee - certainly not one as robust and as effective as Simon Danczuk - can be fettered in the way they give evidence, because they can actually say what they want."

In the House of Commons, Home Office minister Norman Baker said that the Government had made clear that it wants police and prosecutors to bring those responsible for "heinous" historical child sex abuse to justice.

Mr Baker was responding to a question from Liberal Democrat MP Duncan Hames, who asked what steps the Home Office was taking to co-ordinate lessons learnt across Government from investigations into organised sexual abuse of children.

Mr Hames said: "When, in answer to my question last month here, the Prime Minister said he was happy to look at the case for an independent inquiry, I was optimistic. We may not have long to wait now."

But the Cheltenham MP said he was "dismayed" at reports that the Metropolitan Police had assigned only seven officers to look into allegations of an establishment paedophile ring, under the codename Operation Fernbridge.

Mr Baker responded: "We do take these matters extremely seriously and all ministers have made it very plain that we expect the police, the Crown Prosecution Service and others to take all necessary (steps) to bring those responsible for heinous crimes to justice."

He added: "The fact that these matters are getting extra coverage these days, and the fact that the Government has made it very clear that we take these matters seriously, is encouraging people to come forward, including with historical allegations, and that is exactly right.

"We expect the police and Crown Prosecution Service to investigate them properly."

A petition launched by Mr Watson calling for "a national inquiry" into the allegations has now accumulated more than 77,000 signatures online.

Mr Watson, commenting on the change.org petition, said of the Home Secretary's announcement "the devil will be in the detail", calling for the inquiry to be equipped with the necessary powers to delve into the allegations.

He said: "Having talked to a number of survivors and retired child protection specialists I know one thing: if this new inquiry is not given the power to obtain all documents it wants to see, then it won't get anywhere."

Mr Watson, MP for West Bromwich East in the West Midlands, added it had previously emerged police had a file on the late Liberal Democrat MP Cyril Smith, and in 2012 Greater Manchester Police said the politician should have been charged with physically and sexually abusing young boys.

He added: "If police held a file on Smith, then the inquiry team will want to know if they held files on any other individual.

"That's why the power to demand files is vital."