David Cameron remains confident that Baroness Butler-Sloss is the right person to lead the Government's inquiry into allegations that establishment figures conspired to cover up child abuse, Downing Street has said.
The former High Court judge faced calls to step down after reports that her brother Sir Michael Havers tried to prevent ex-MP Geoffrey Dickens airing claims about a diplomat in Parliament in the 1980s.
"I know absolutely nothing about it," she told the BBC. "If people think I am not suitable, then that's up to them."
The Home Office said Lady Butler-Sloss's integrity was "beyond reproach" and it stood "unreservedly" by her appointment.
Asked whether Mr Cameron was confident she should head the inquiry, the Prime Minister's official spokesman told a Westminster media briefing: "Yes. She commands the very highest respect for her professional expertise and integrity.
"His view is that she does command widespread respect and confidence, and rightly so."
Following Lady Butler-Sloss's appointment yesterday, there have been growing expressions of concern that the cross-bench peer is too closely tied to the establishment to carry out the inquiry announced by Home Secretary Theresa May this week.
Labour MP Simon Danczuk, whose questions helped put the issue centre-stage, said: "We want somebody in the chair that exudes confidence and that's not the case. She is part of the establishment and that raises concerns, and the relationship in terms of her brother, I think, is too close for comfort. I think that's the conclusion most people will reach.
"I think the Government should think again in terms of who they have appointed for this position."
Sir Michael - a barrister and MP who became Lord Havers before his death in 1992 - is said to have had a 20-minute argument outside the Commons chamber with Mr Dickens in the 1980s in an attempt to stop him using parliamentary privilege to name diplomat Sir Peter Hayman as a paedophile.
Mr Danczuk added: "I think she should consider her position. I find it quite surprising that neither she nor the Government realised her relationship with her brother was connected to Geoffrey Dickens and all the palaver around it.
"It beggars belief that that hadn't been considered in the first place."
Conservative Sarah Wollaston, who chairs the Commons Health Select Committee, said she did not doubt the peer's integrity but it was "hard to see why Baroness Butler-Sloss would want to accept a role so many regard as conflicted at the outset".
Home Affairs Select Committee chairman Keith Vaz has expressed surprise at the selection, pointing out that while Lady Butler-Sloss is "distinguished", she is also a member of the House of Lords.
But the Home Office said Lady Butler-Sloss's integrity was "beyond reproach" and it stood "unreservedly" by her appointment.
And in a written statement to MPs, Mrs May said: " Baroness Butler-Sloss brings with her many years of experience in the field of child protection and law, and I am confident that she will deliver the thorough, robust and independent review that I have promised.
"To ensure that the terms of reference for the inquiry are sufficient to deliver the robust review which is required, I have asked that Lady Butler-Sloss agree the final terms of reference with the full panel, when appointed. The inquiry will begin its work as soon as possible after the appointment of other members of the panel and I shall provide a further update in due course."
Mr Cameron's spokesman declined to say whether Lady Butler-Sloss's relationship to Lord Havers had been discussed during the process of picking an inquiry chair.
"The focus was on finding a person with the right expertise and integrity," said the Prime Minister's spokesman. "That's exactly what we have in Elizabeth Butler-Sloss."
Asked whether Mr Cameron considered her family relationships relevant to her appointment, the spokesman said: "There has been no change in the Government's and the Prime Minister's view about her suitability for the role."
Alison Millar, head of the abuse team at law firm Leigh Day, which represents alleged victims of abuse at institutions that will be examined by the inquiry, said: " Whilst Lady Butler-Sloss is a person of enormous integrity, the concern really is that she is just too close to the establishment and, in particular, concern over her family connection to Sir Michael Havers.
"Justice must be seen to be done by those who are understandably the most reticent to come forward, those who have survived abuse.
"The panel needs to be reconsidered and must involve those working in the area of child abuse as well as survivors of abuse now working in that area."
Mrs May attempted to take the initiative in the furore this week by announcing two separate inquiries - one broad Hillsborough-style investigation led by Lady Butler-Sloss, and another into the historic issues at her own department.
The Home Office said today: "Baroness Butler-Sloss has had a long and distinguished career at the highest levels of this country's legal system.
"Her work leading the Cleveland child abuse inquiry and as president of the High Court's Family Division make her the perfect person to lead this important piece of work.
"As the permanent secretary told the Home Affairs Select Committee yesterday, the integrity of Baroness Butler-Sloss is beyond reproach and we stand by her appointment unreservedly."
Former home secretary Lord Brittan has flatly denied failing to deal properly with a dossier about the allegations provided by Mr Dickens in 1983, while a review carried out by an HMRC official last year found no evidence that relevant material was not passed to other authorities.
It also disclosed that the Dickens file appeared to have been destroyed - and it has since emerged that 114 files deemed potentially relevant are missing.
Former detective Terry Shutt was involved in the arrest of paedophile Peter Righton, a former consultant to the National Children's Bureau, but claims important material uncovered in the case was not followed up.
Righton, who is now dead, was a founding member of the Paedophile Information Exchange (PIE) before he was convicted of importing child pornography.
Mr Shutt, who served with West Mercia Police, told the BBC that suitcases of letters found in Righton's home pointed to a wider network of child abusers.
"In amongst all the other documentation there was a definite link to establishment figures, including senior members of the clergy," he said. "So, for me, there was a definite feel that this was something bigger than we were looking at locally and it should be investigated further."
Mr Shutt said some arrests were made but he was "confident that the main link into the establishment" was not followed up.
"At the time there was a culture to protect the establishment. It was seen to be more important to protect the establishment than to deal with individuals who had transgressed," he said.
Shadow Attorney General Emily Thornberry questioned the appointment of Lady Butler-Sloss.
She told BBC Two's Daily Politics programme: "Her brother was Lord Havers, her brother was Attorney General.
"Geoffrey Dickens gave two dossiers - he gave one to the Home Office and gave the other one to the DPP (Director of Public Prosecutions) - and the DPP copy has also gone missing and at the time the DPP was answerable to the Attorney General.
"I don't question this admirable extraordinary woman's integrity... But I'm surprised the Home Office didn't look at this, because I think they have put her in a very difficult position."
Asked whether Labour thought Lady Butler-Sloss should head the inquiry, a senior party spokesman said: "Our concern is that the victims have confidence in the ongoing inquiry.
"She has a very fine record on child abuse issues and in the family courts. It should be for the Home Office to ensure that victims have confidence and that this can go forward."
Labour highlighted the fact that Home Office minister Damian Green first informed MPs of the 114 missing files nine months ago, and demanded to know why Mrs May had not acted at that point.
In a written response on October 9 2013 to a question from Labour MP Tom Watson about the progress of the review of Home Office files relating to child sex abuse, Mr Green said: "Out of an extensive analysis of a central database containing details of over 746,000 files for the 1979 to 1999 period, 114 potentially relevant files had been presumed destroyed, missing or not found."
A Labour spokesman said: "It's a fair question to ask when was Theresa May first aware of this. Was it in October last year? If not, why not? If she was aware of it, what action did she take?
"It's a fair question when David Cameron knew about the missing files and if he was aware, what did he do?"
Actor Nigel Havers, son of Lord Havers and Lady Butler-Sloss's nephew, defended his aunt's appointment.
He told BBC Radio 4's World at One programme: "I know my aunt very well and had she felt any form of bias or any idea that she shouldn't be doing this inquiry she would have pulled out this morning.
"The very fact that she hasn't means to me that she feels she has absolutely had no political ties to my father and knew nothing about what was going on in the House of Commons at that time and therefore she has every right to, I think, continue to lead the inquiry."
Havers said Lady Butler-Sloss was "totally honest, totally transparent, highly respected and very, very good at her job".
"I don't think the fact that my father was attorney general at the time makes any difference whatsoever," he added.
Havers said he had never discussed the claims now being made with his father at the time.
"I was blissfully making movies or doing my job and I didn't really have a great deal of interest in politics at the time except that I know that he worked very hard and was very close to what was going on in government but, as you said, he is not around to defend himself," he added.
Asked if Labour supported Lady Butler-Sloss's appointment, Shadow Culture Secretary Harriet Harman told World at One: "It's a Home Office appointment, it's not our appointment, but we are supporting it being as open and transparent as possible and we absolutely respect Elizabeth Butler-Sloss, but we are determined that we do think that the victims must have confidence in it and perception is important."
Ms Harman said the inquiry "obviously" should look into PIE, which had links to the National Council for Civil Liberties while she worked there.
"The thing about PIE, which was so pernicious about it, is that they infiltrated organisations, so they infiltrated social work organisations, they infiltrated even the Home Office as it turns out, and obviously that is deeply regrettable," she added.
"What they did is they said they were just for free speech and talking about sexual identity, but actually what they were doing was covering up for their own evil child abuse.
"So, yes, I'm sure that the whole issue of PIE will be looked at in this inquiry. They were a very evil organisation."
Shown a picture of an advert for the NCCL in a PIE magazine from the 1970s, she said: "Obviously it is very regrettable that they even existed and peddled that line of argument, but worst of all that they were perpetrating abuse."
The Green Party said Lady Butler-Sloss must step aside and a "credible" figure from outside the circles being investigated brought in.
Leader Natalie Bennett said: "It is unacceptable that Lady Butler-Sloss oversee an inquiry into a possible cover-up of paedophile activities at Westminster in the 1980s given that her brother, Sir Michael Havers, was attorney general at the time. She must step aside.
"However unimpeachable Lady Butler-Sloss's reputation may be, justice must be seen to be done and conflicts of interest like this cannot be tolerated.
"No one should be expected to investigate a close member of their own family as part of an official inquiry. The Green Party believes that only a credible figure from outside the circles being investigated will have the trust of the public to look into the alleged systematic sexual abuse of children by politicians and other members of the establishment."