Lord Tebbit has said he believes there may have been a political cover-up of child abuse allegations against politicians in the 1980s as Theresa May came under pressure to explain how the Home Office lost or destroyed more than 100 files related to accusations of organised paedophilia.

The former cabinet minister, who served under Margaret Thatcher, said the collective instinct of establishment figures at the time was to protect "the system" and not to delve too deeply into claims.

The home secretary is preparing to make a statement to the House of Commons on Monday to explain what happened to the missing documents relating to historic organised child abuse over a period of 20 years.

Ministers hope this will quell demands for a public inquiry into disparate allegations of child abuse from that era. They include claims of abuse against the late Liberal MP Cyril Smith and allegations of paedophile activity at parties attended by politicians and other prominent figures.

The missing Home Office material is reported to include details of officials, MPs and peers all implicated in child sex abuse, including one Conservative MP at the time who was reportedly found with child pornography but subsequently released by the police.

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."

Asked on the BBC's Andrew Marr programme if he thought there had been a political cover-up at the time, Tebbit said: "I think there may well have been. It was almost unconscious. It was the thing that people did."

May will make a statement to the House which, it is understood, will try to shed light on the process by which her department will investigate the missing files and their content. Government sources said she may also address claims of a cover-up.

On Sunday night petition organised by the Labour MP Tom Watson calling for a national inquiry into allegations of organised child abuse had gathered more than 53,000 signatures.

The permanent secretary at the Home Office, Mark Sedwill, will be appointing a senior legal figure to conduct a fresh review into what happened to a dossier relating to alleged paedophile activity at Westminster which was passed to the home secretary, Leon (now Lord) Brittan in 1983 by the Tory MP Geoffrey Dickens, who died in 1995. Brittan has since said he passed the document on to officials in the home office to investigate.

In a letter to the Commons home affairs committee, Sedwill disclosed that a previous review – carried out last year – 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 investigation had also identified 13 "items of information" about alleged child abuse, nine of which were known or reported to the police at the time – including four involving Home Office staff. Police had since been informed of the other four cases.

Sedwill, who will appear before the home affairs select committee on Tuesday, said he had ordered the new investigation – after the intervention of David Cameron – to establish whether the findings of the previous review remained "sound".

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.

Shadow home secretary, Yvette Cooper, said the "review of a review" announced by Sedwill was insufficient. "We need a wide-ranging review that can look at how all the allegations put to the Home Office in the 1980s and 1990s were handled," she wrote in a letter to May.

"The scope of this investigation must look at how the Home Office, other parts of Whitehall, the police and prosecutions agencies, handled allegations when they were put to them. But it also needs the flexibility to follow the evidence.

"Any stones left unturned will leave concerns of institutional malaise, or worse, a cover-up, unaddressed."

Ministers appeared to be unsure whether a public inquiry might be held in the future. The Cabinet Office minister Francis Maude said the government understood the need for openness "so that there can't be any hint of a cover-up".

Separately, reports have claimed that Brittan has been interviewed by police over an allegation of rape related to an incident in 1967 before he was an MP. The alleged victim, a woman, was an adult at the time of the alleged incident. Brittan strongly denies the allegation. In a statement, Scotland Yard said in late 2012 a woman claimed to police that she was raped by a man at an address in the capital.

Police added that a man in his 70s was interviewed under caution last month.