London: The new chairman of a long-awaited government inquiry into historic child sex abuse was facing calls to resign Sunday night after The Mail on Sunday discovered her astonishing links to Leon Brittan — a key figure embroiled in the scandal.

Lord Mayor of London Fiona Woolf was appointed to carry out the important role of investigating claims of an Establishment cover-up of VIP paedophile rings on Friday, two months after the original chairman was forced to step down over conflicts of interest.

But it has been found that the top corporate lawyer is also closely linked to Lord Brittan — who is likely to give evidence to her inquiry. It can be revealed that she:

Sits on the board of a City of London conference with Lord Brittan, who is accused of overseeing an Establishment cover-up when he was Home Secretary;

Judges an annual City award scheme alongside Lord Brittan’s wife, Diana;

Gave Lord Brittan’s wife a £50 donation and a friendly good-luck message when she took part in a charity fun run last year;

Has been a neighbour of Lord and Lady Brittan in the same exclusive London street for the past decade;

Is a governor of the elite Guildhall School of Music where pupils are said to have been abused;

Is a patron of a body for female lawyers along with Labour’s Harriet Harman, whose National Council of Civil Liberties once had links to a notorious paedophile group.

Sunday night Labour MP Simon Danczuk — who has led calls for a public inquiry into historic child sex abuse in the wake of revelations about high-profile figures such as Jimmy Savile — questioned Woolf’s appointment. “If it’s found that Fiona Woolf is close to the Brittans, her position is untenable and she needs to be clear about what her relationship is with Leon Brittan, who is one of the most significant figures in terms of suggestions of a cover-up,” he said. “Surely the Home Office was aware of this before they suggested appointing her?”

Peter Saunders, chairman of the National Association for People Abused in Childhood, said: “It would once again seem to be incredibly inappropriate that she would even be offered the appointment.”

Home Secretary Theresa May, who personally appointed Mrs Woolf after her background was checked by officials, was also facing questions about her judgement. Last night it was not clear if she had been made aware of Woolf’s close association with the Brittans.

Labour MP John Mann said: “If Fiona Woolf is friends with Leon Brittan, that is a problem. If that’s the case, she shouldn’t have accepted the job. She needs to move straight away to clear the air — it would be a catastrophe to lose a second chair.

“The Home Office also needs to clear the air and demonstrate that it did due diligence.’

And Labour MP Keith Vaz said he would call Woolf to give evidence before his influential Home Affairs Select Committee, adding: “I am sure she will want to be as open and transparent as possible.”

The public inquiry was announced in early July, following months of pressure from MPs and campaign groups as more and more claims emerged of secret VIP sex rings across Britain and child abuse in schools, hospitals and churches, dating back more than 30 years, with the perpetrators spared justice by an Establishment cover-up.

It suffered a massive setback within weeks when the chairman, former High Court judge Baroness Butler-Sloss, was forced to quit over conflicts of interest. Over the summer, the Home Office has been searching for a suitable replacement whose experience and background would command respect from victims and Westminster, while also having the required distance from the individuals and institutions they will have to scrutinise.

On Friday, it was announced that Woolf had been appointed, with the aim of publishing an interim report before next May’s General Election.

Woolf said she was “honoured” and added that learning from the mistakes of the past was a “vital and solemn undertaking”.

But MoS research soon suggested the Home Office had not learnt from its own mistakes. Publicly available documents revealed that Woolf, 66, has several close links to former Home Secretary Lord Brittan and his wife.

It calls into question her ability to run the inquiry because earlier this year Lord Brittan was at the centre of a storm over an alleged cover-up of child sex abuse and a missing list of alleged VIP paedophiles.

He admitted he had received the so-called ‘Dickens dossier’ from campaigning MP Geoffrey Dickens in 1983 but insisted he had passed the papers on to Home Office officials.

It then emerged he had recently been questioned by Scotland Yard over allegations that he raped an 19-year-old in 1967. He denies the claims and has not been arrested or charged.

The Home Office last night refused to answer questions about what it had known about Woolf’s links to Lord Brittan.

The Brittans yesterday refused to answer questions from the MoS as they drove away from their home.

Woolf could not be reached.