The woman heading Britain's inquiry into historic claims of child sex abuse by politicians resigned Monday less than a week after her appointment, following criticism over her establishment links.

Retired British judge Elizabeth Butler-Sloss came under fire because of a potential conflict of interest, as the investigation will likely look at the handling of allegations by her brother, a former attorney general.

Prime Minister David Cameron's office said it was "entirely her decision" to step down as lead investigator into allegations of how police and prosecutors handled claims of sexual abuse in the highest levels of Britain's political establishment during the 1970s, 1980s and 1990s.

Long-running rumours about a paedophile ring involving senior politicians have taken on new significance in Britain following a string of scandals about abuse by celebrities including late BBC star Jimmy Savile.

In a statement explaining her decision, Butler-Sloss, 80, acknowledged that she "did not sufficiently consider" the impact of her family connections when she accepted the appointment last Tuesday.

"It has become apparent over the last few days... that there is a widespread perception, particularly among victim and survivor groups, that I am not the right person to chair the inquiry," she said.

"It has also become clear to me that I did not sufficiently consider whether my background and the fact my brother had been attorney general would cause difficulties."

Her late brother Michael Havers, father of actor Nigel Havers, is alleged to have tried to prevent a former lawmaker from airing claims about a diplomat in parliament in the 1980s, when he was attorney general.

Another victim also alleged that Butler-Sloss kept claims against a bishop out of a 2011 review into how the Church of England dealt with two paedophile priests because she "cared about the Church".

Lawyers for the victims had immediately attacked the appointment, and said they were "relieved" by Monday's announcement.

Alison Millar, head of the abuse team at law firm Leigh Day that is representing alleged victims, said its clients were "pleased and... relieved" by the news.

"This was the only sensible decision to ensure that survivors and the public could feel confident that the inquiry was not going to be jeopardised by accusations of bias," she said in a statement.

"The issue was never the integrity of Lady Butler-Sloss or what she knew of her brother's actions as the chief legal advisor to the government, it was always the fact that she would ultimately have to judge those actions."

Cameron's office brushed off claims that the news was an embarrassment to the government, and stood by its original decision.

"The reasons for her appointment still absolutely stand, her professional expertise, her integrity I don't think has been questioned from any quarter whatsoever," a spokesman said.