The government's child abuse inquiry has been pitched back into crisis with the prime minister's judgment again in question amid growing demands for the newly-appointed chairman, Fiona Woolf, to stand down.

Labour has declared her position is no longer viable, and there has been a demand for a judicial review into her appointment after her links with former Tory Home Secretary Leon Brittan were revealed.

Lord Brittan was in post during the 1980s when a dossier on an alleged paedophile ring operating in and around Westminster was handed to him by campaigning former MP Geoffrey Dickens.

There have been persistent claims the issue was covered up, though Brittan has denied failing to take any action over the dossier, some of which has since gone missing.

It has now emerged that Woolf attended two dinners at Brittan's home and hosted him and his wife on three other occasions.

David Cameron is now caught on a hook, forced to offer full support for Woolf for fear of losing the second chairman of the inquiry before it has even started its work.

To allow her resignation would lead to claims the prime minister and home secretary Theresa May had either failed to do "due diligence" on the appointment, or had displayed lack of judgement in going ahead with it.

The inquiry was first thrown into disarray when the original chairman, Baroness Butler-Sloss was forced to resign after it emerged her late brother, Lord Havers, was attorney general at the time of the original allegations.

But as the pressure on Woolf intensified, the prime minister was forced to again insist she had his full confidence.

His spokesman said: "The prime minister's message is robust and clear. There is no change. He has full confidence in Fiona Woolf and looks forward to her leading the inquiry."

Earlier he had said: "If you look at her background [as president of the Law Society], she brings experience and expertise to the role as head of the panel," adding there had been a process of due diligence.

The whole inquiry has proved a nightmare for the government, with the resignation of Butler-Sloss, claims it could last for many years, lack of confidence from victims, and persistent suggestions key pieces of evidence have gone missing.