The former Conservative cabinet minister Lord Tebbit has said he believes there "may well" have been a political cover-up over child abuse in the 1980s.

Norman Tebbit, who served in a series of ministerial posts under Margaret Thatcher, said the instinct of people at the time was to protect "the system" and not to delve too deeply into uncomfortable allegations.

His comment came as the Home Office announced a fresh legal review into what happened to a file alleging paedophile activity at Westminster in the 1980s that was handed to the then home secretary, Leon (now Lord) Brittan, by the Tory MP Geoffrey Dickens.

But as it emerged on Sunday that a further 114 possibly relevant files have also gone missing from government records– the government again ruled out a public inquiry into the allegations.

Michael Gove told the BBC1's Andrew Marr Show that the inquiry, to be led by a senior lawyer, would suffice, highlighting the fact that there were ongoing criminal inquiries. He said that he and the health secretary, Jeremy Hunt, were also reviewing current child protection practice to ensure that children were properly protected.

Also appearing on The Andrew Marr Show, Tebbit said: "At that time I think most people would have thought that the establishment, the system, was to be protected and if a few things had gone wrong here and there that it was more important to protect the system than to delve too far into it.

"That view, I think, was wrong then and it is spectacularly shown to be wrong because the abuses have grown."

Asked if he thought there had been a "big political cover-up" at the time, he said: "I think there may well have been. But it was almost unconscious. It was the thing that people did at that time."

The missing dossier compiled by Dickens is thought to have detailed allegations of a 1980s Westminster paedophile ring and is now known to be one of 114 potentially relevant Home Office files destroyed, lost or missing, it has emerged.

David Cameron has already ordered Mark Sedwill, permanent secretary of the Home Office, to look into what happened to the lost dossier but the revelation that further relevant documents have disappeared will raise fresh fears of an establishment cover-up.

Simon Danczuk, the MP for Rochdale, who is calling for an overarching national inquiry into historical child abuse, said: "I had absolutely no idea these other files were also missing. The public view will be that there is something fishy going on. The public will understandably think these documents have gone missing because it helps protect the names of those identified in them. That is the conclusion that many will come to, and who could blame them."

Tom Watson, the Labour MP central to the uncovering of the phone-hacking scandal, said it was increasingly clear that only a Hillsborough-style inquiry would reassure the public. He said: "Only an overarching inquiry will get to the facts, everything else the government says or does on this is a diversion."

Dickens, who died in 1995, had told his family that the information he handed to the home secretary in 1983 and 1984 would "blow the lid off" the lives of powerful and famous child abusers, including eight well-known figures.

In a letter to Dickens at the time, Brittan suggested his information would be passed to the police, but Scotland Yard said it has no record of any investigation into the allegations. On Saturday, the Home Office made public a letter to Keith Vaz, the chairman of the home affairs select committee, in which the department confirmed that correspondence from Dickens had not been retained and it had found "no record of specific allegations by Mr Dickens of child sex abuse by prominent public figures".

Sedwill admitted, however, that a further 114 documents relevant to allegations of child abuse were missing from the department's records. That discovery was made last year by an independent review into information received about organised child sex abuse but was not published in its report. Sedwill told Vaz that the missing documents were some of the 36,000 records that officials presumed were lost, destroyed or missing. They were not part of the 278,000 documents the Home Office destroyed as part of its "retention and destruction" policy.

However, Sedwill told Vaz in a letter published on Saturday that the department had found "no evidence of the inappropriate removal or destruction of material".

He also wrote to the prime minister to tell him he would engage a senior independent legal figure to assess whether last year's conclusions "remain sound".

Sedwill told Vaz: "Like any other citizen, I am horrified by what we have learned in the past couple of years about the systematic abuse of children and vulnerable adults by prominent public figures, and the state's failure to protect them. Some have been brought to justice, and I hope that the police investigations now under way across the country are equally successful. The Home Office has and will cooperate fully with any police inquiry."

Vaz said the number of files lost were on an "industrial scale". He told BBC Breakfast that he welcomed the letter from Sedwill, adding: "We will want to pose further questions, of course, because there's a lot of information that we didn't know was in existence that he's given us in this letter.

"But also I think that the government and Mr Sedwill should work with parliament in fashioning a set of terms of reference that will satisfy all those who are dissatisfied with the way in which matters have been progressed so far - so I think it's an important step which we welcome."

Margaret Hodge, the Labour MP who chairs the public accounts committee, criticised the "veil of secrecy" over the issue.

Appearing on Sky News's Murnaghan programme, she added: "Thank God it is coming out into the open. I think the really interesting thing about it is there has been a veil of secrecy over the establishment for far too long.

"Now the establishment, who thought they were always protected … find actually they are subject to the same rigours of the law, and that's right.

"What we really need to get right as well is how children are cared for today. Let's learn from the historic abuse, let's actually give victims the right to have their voice on that, but let's actually also focus on the present."