One of Britain’s most eminent lawyers urged the Prime Minister to give the unwieldy investigation a major overhaul. Veteran barrister Michael Mansfield, QC, said he would consider acting as co-chairman of the investigation which he said badly needed shaking up.

He spoke after lead counsel Ben Emmerson, QC, and first junior counsel Elizabeth Prochaska both stepped down.

As chairwoman Alexis Jay was dealing with the resignations, the inquiry was dealt a further blow as it faced a challenge from the family of the late Lord Janner. Allegations against the former Labour MP are the subject of one of the 13 separate investigations by the inquiry.

Lord Janner’s family fear public sessions will descend into a kangaroo court with no chance to cross-examine alleged victims. Mrs May was Home Secretary when she set up the Independent Inquiry into Child Sex Abuse two years ago.

Ex-social worker Professor Jay became the £185,000-a-year head of the most ambitious public inquiry in UK history in August after three previous chairwomen quit.

Many experts fear the inquiry is already dead in the water and former director of public prosecutions Lord Macdonald said it should be either constrained or closed. But Mr Mansfield said today: “This has been chaotic from the beginning... there should have been far more consultation not just about the terms of reference but about how it’s going to be managed.”

Mr Mansfield said a lawyer should be appointed to help Professor Jay. Asked if he would take up the post, he said: “I’m very willing to consider it... they need another lawyer at the top because there are legal decisions to be made and I’m afraid the present chair isn’t a lawyer.

“One person cannot possibly cope with this as an over-arching inquiry.”