The public inquiry into child sexual abuse has come under pressure to establish whether or not allegations against senior politicians are well founded, as its attention turns to the world of politics.

Opening the Westminster strand of the independent inquiry into child sexual abuse (IICSA) on Monday amid claims of “witch-hunts” and “moral panic”, the counsel for the inquiry said it would examine how political parties reacted to paedophilia claims against their members, including the late Liberal MP for Rochdale Cyril Smith and the late Conservative MP for Chester Peter Morrison.

A third case study will look at David Challenor who, the inquiry heard, was allowed to remain an active member of the Green party before being jailed for 22 years last year after being convicted of torturing and raping a 10-year-old girl.

Before the hearing began, however, the inquiry was criticised for being a “witch-hunt against dead politicians” by the family of the late Labour peer Lord Janner. The claims against Janner will be examined in a different strand of the inquiry, the hearing heard.

The lead counsel, Brian Altman QC, said the inquiry will examine how the whips’ offices have operated in parliament, including “whether it is true that the whips’ offices of any party failed to report or, worse, assisted in suppressing allegations or evidence of child sexual abuse”.

It will also look at the honours system, following concerns about “honours granted to individuals who had been accused of child sexual abuse”.

The Westminster strand is one of 13 being considered by the inquiry, which began in 2015 following the Jimmy Savile scandal. There followed a string of claims against both living and dead politicians.

Altman told the London hearing the inquiry will not consider allegations made by Carl Beech, who had been known as “Nick”, claiming there was a Westminster paedophile ring operating in Dolphin Square. Beech has since pleaded not guilty to charges of perverting the course of justice and fraud.

“It is our firm submission that public concern over Westminster child sexual abuse allegations neither begins nor ends with Mr Beech,” Altman said.

“We suggest, and we are confident that many of the core participants here today will agree, that there are outstanding questions of public concern in this area that it is both necessary and appropriate for this inquiry to investigate.”

Altman said a question raised by Labour’s Tom Watson in the Commons in 2012, saying there was “clear intelligence suggesting a powerful paedophile network linked to parliament and No 10”, could be seen as the “catalyst for the establishment of this inquiry”.

Geoffrey Robertson QC, who represents the former Conservative MP Harvey Proctor, condemned the intervention of the deputy Labour leader.

“This inquiry has detected a number of cover-ups – over Sir Peter Hayman [a former diplomat who was a member of the Paedophile Information Exchange] and Cyril Smith – but the moral panic started by Tom Watson has no basis. It was smoke without fire,” he said.

Robertson called on the inquiry to clear the names of those, such as Proctor, who have been wrongly accused of abuse.

The QC also suggested libel laws needed reform because they had protected abusers such as Savile, and said police seeking a search warrant should need permission from a full-time district judge, rather than obtaining the go-ahead from a “favourite” lay magistrate.

Richard Scorer, a solicitor at the law firm Slater and Gordon who represents seven men who have made allegations against Smith, said the culture of safeguarding children had to be embedded in political parties. “The prime concern was reputational risk … No one ever seems to consider whether there are children at risk,” he said.

Sam Stein QC represents a former civil service consultant, Tim Hulbert, who claims he saw evidence of Home Office funding of the Paedophile Information Exchange in the late 1970s. The funding, he alleges, was channeled through the Women’s Royal Voluntary Service because Special Branch wanted to monitor PIE members.

“We suggest that the Home Office must explain the missing [financial] records relating to millions of pounds of missing money,” Stein told the inquiry.

Samantha Leek QC, who represents the Metropolitan Police Service, told the inquiry that an 80-strong unit – Operation Winter Key – which has been looking into allegations that detectives had been prevented from carrying out investigations, had not come up with proof of any cover-ups so far. “The assessment made by the MPS is that there’s insufficient evidence in any case to bring criminal or disciplinary action,” she said.

Representatives of MI5, the Metropolitan police and the Independent Office for Police Conduct will also be called as witnesses during hearings this month.

The IICSA has stressed that allegations against people accused of wrongdoing during the hearing are not necessarily true.