David Cameron has asked the Home Office's most senior civil servant to investigate what happened to a missing dossier of alleged paedophile activity involving politicians in the 1980s.

The request follows pressure from former ministers and campaigners to find the dossier, which was handed to the then home secretary, Leon Brittan, by the Conservative MP Geoffrey Dickens.

Cameron said he understood the concerns that had been raised. "That's why I've asked the permanent secretary at the Home Office [Mark Sedwill] to do everything he can to find answers to all of these questions and to make sure we can reassure people about these events.

"So it's right that these investigations are made. We mustn't do anything, of course, that could prejudice or prevent proper action by the police. If anyone has information about criminal wrong-doing they should, of course, give it to the police," he said.

But Simon Danczuk, the Labour MP who exposed the late Liberal MP Cyril Smith as a paedophile, said another internal inquiry was a case of trying to limit the damage, and would not win back the public's confidence.

The MP for Rochdale said: "[Cameron's] statement today represents little more than a damage limitation exercise. It doesn't go far enough. The public has lost confidence in these kind of official reviews, which usually result in a whitewash. The only way to get to the bottom of this is a thorough public inquiry."

Dickens, a longstanding campaigner against child abuse, passed the dossier of allegations to Brittan in 1983. Brittan has said he passed it on to his officials and raised concerns about some of the allegations with the director of public prosecutions.

Following claims last year by the Labour MP Tom Watson that a paedophile ring existed at Westminster, Sedwill commissioned a review into historical abuse claims against politicians. It found that the dossier had not been retained "in line with departmental policy" and concluded the Home Office "acted appropriately, referring information received during this period to the relevant authorities".

The Daily Telegraph has reported that the dossier included the name of a former Tory MP who was found with child pornography videos but no action was taken. It was claimed Customs officers stopped the politician at Dover while he was returning to the UK by car. He was found to have explicit videos of children "clearly under 12" but was not arrested or charged and the videos and paperwork have subsequently gone missing. The customs officer is said to have spoken to detectives on Operation Fernbridge, an investigation into allegations of sexual abuse.

Watson, who has led calls for a comprehensive inquiry into historical child abuse, said he was writing to the director of public prosecutions, Alison Saunders, to ask her to examine the evidence relating to the unnamed politician.

The Metropolitan police said: "We are not prepared to give a running commentary on Operation Fernbridge, which is an ongoing operation."

It has emerged that four more cases of historical sex abuse have been referred to the police by Home Office officials in recent months following a review ordered last year covering the period from 1979-99.

A review of a database containing details of more than 746,000 files identified 13 items of information about alleged child abuse, including four cases involving Home Office staff. Nine of these items, including the four involving Home Office officials, were either already known to the police or were reported to them by the Home Office at the time. The remaining four have now been passed to the police for a "proper assessment", although the investigator who carried out the review said the information was likely to be of limited value.

A Home Office spokesman said: "In response to concerns raised in parliament and the media relating to the handling by the department of historical allegations of abuse, the permanent secretary commissioned an independent review of all relevant papers received by the department between 1979 to 1999 to identify any information received and the outcome.

"The review concluded the Home Office acted appropriately, referring information received during this period to the relevant authorities."