It also emerged that the peer was responsible for a controversial ruling which prevented warnings being issued about dangerous paedophiles.

Senior social workers attacked her decision – made when she was an Appeal Court judge – and warned that it would have “major ramifications”.

Home Secretary Theresa May will be questioned about the appointment this afternoon when she appears before the Commons home affairs committee.

While saying publicly that the inquiry must enjoy public confidence, the Labour leadership has stopped short of joining calls for Lady Butler-Sloss to be removed as the head of the inquiry panel.

But Ms Baird, the Northumbria Police commissioner, said her position was untenable.

"I don't think her personal qualities could be in contention here. Her suitability is pretty immaculate," she told BBC Radio 4's Today programme.

"The difficulty is that she is, through her family, linked to the very establishment that this inquiry is being set up to look at.

"I have no reason to know anything at all – there are rumours everywhere about this – as to whether Michael Havers was ever given any information or whether he acted upon it or it didn't.

"But she is going to have to investigate the role played by her late brother.

"If she were in a court case, presiding over it, and her brother was mentioned as someone she may have to investigate as to his role, she would of course withdraw due to a conflict of interest.

"The conflict of interest is even bigger here where we have a vulnerable community of people who say they have been not allowed to get justice.

"It has got to be done by somebody who is an outsider to this, who is completely independent."

She went on: "Should somebody be investigating something in which their brother has been named, however, in due course, he may be exculpated?

"Is this going to satisfy this very vulnerable company of people who feel that the establishment's kept them out of justice already?

"I think it is an error. I don't know if she, when agreeing to take it on, knew the implications for herself and for her family. She is a very dutiful person and would feel she should take it on if she was asked to do so.

"The error is the Home Secretary's and it needs correcting."

Lady Butler-Sloss led a panel of three judges who overturned a previous ruling which said councils could warn other local authorities about two men who had been found to have had inappropriate relationships with children.

Neither man had been convicted in a criminal court but in civil proceedings judges had ruled they had been involved in improper sexual relationships with children.

One man, who can only be identified by the initial ‘L’, then 36, was acquitted of attempting to rape his step-daughter and of indecently assaulting his five children but care proceedings in the family courts later found he had been responsible for sexual abusing three children in his care.

He posed a “significant risk” to the three youngest children, the court held.

Croydon council, in south London, where L had lived, sought to secure L’s new address from the court to alert the local authority about his sexual behaviour.

A judge ruled in 1997 that Croydon could go ahead but Lady Butler-Sloss overturned that decision the following year.