The Independent Inquiry into Child Sexual Abuse (IICSA) is reviewing whether to continue an investigation into historic allegations against the late Lord Janner.

A three-week hearing into the case of the former Labour MP had been scheduled for October this year.

The inquiry, which was set up to examine whether public institutions had failed to investigate child abuse, is meant to hold its sessions in public.

But after one of the complainants against Lord Janner wanted to remain anonymous, the IICSA was faced with a dilemma.

Leading counsel to the inquiry Brian Altman said its chairman, Professor Alexis Jay, was left with three options: either to hold most of the hearing into the Janner case in closed session, discontinue it altogether or restrict it to a few limited issues in public.

In 2014 Leicester Police said there was enough evidence to bring charges of historic sex abuse of under-age boys against Lord Janner but the Crown Prosecution Service said the following year he was unfit to stand trial because of his dementia.

At the time of his death aged 87 in late 2015, the allegations against him were due to go to a “trial of the facts”, where juries consider the evidence, without convicting.

The family of the former President of the Board of Deputies has maintained his innocence.

His case was the only one of an individual rather than an institution to be taken up by the IICSA.

Its remit is to look into whether police and the CPS on three previous occasions had failed properly to investigate allegations against Lord Janner and whether he had enjoyed preferential treatment because of his status.

At a preliminary hearing on Thursday, Daniel Friedman, representing Lord Janner’s daughters Marion and Laura, argued it would be unfair to hold closed sessions because evidence could not be tested in open court.

Arguing that the inquiry should drop the Janner strand, he said, “There was no conspiracy, no cover-up, and no institutional failing. Prominence was irrelevant. Greville Janner did not seek different treatment and nor was he granted it.”

Mr Friedman added, “It is important to recognise now that the experience of the investigation hanging over the family for five years has been a ghastly invasion of their grief.”

But Nick Stanage, representing 14 of the peer’s alleged victims, said that Lord Janner’s family had “never taken a realistic view of the evidence that was said to be capable of  justifying a conviction”.

Professor Jay is expected to announce her decision next month on how or whether to proceed.