The inquiry into historic child sex abuse has been thrown into chaos after the chairman announced she was stepping down in the face of a barrage of criticism.
Fiona Woolf said she had no choice but to quit after accepting the victims had lost all confidence in her ability to conduct the investigation impartially.
It follows sustained pressure over her links with the former home secretary, Lord Brittan, who is facing claims that he failed to act on a dossier of paedophile allegations in the 1980s.
Her departure is a huge blow for the Government after the previous chairman, Baroness Butler-Sloss, also had to quit because her late brother, Sir Michael Havers, was attorney general during the same period.
Mrs Woolf told the BBC that it has been clear to her for some time that she did not have the confidence of the victims and that she should now "get out of the way".
"Ultimately what turned the tide was less about putting up with the innuendo and negative comment in the press, but more about the victims themselves. This is for them," she said.
"I am obviously sad that people are not confident in my ability to chair what is a hugely important inquiry impartially. I don't think it was going to be possible for me to chair it without everybody's support."
Her announcement came after victims' representatives issued a unanimous call for her to be replaced following a meeting with the inquiry panel's secretariat.
Following a bruising appearance before the Commons Home Affairs Committee earlier this month, Mrs Woolf said that she had realised the writing was on the wall after lawyers for the victims demanded a meeting.
"I made my decision a few days back and warned the Home Office of it," she said.
Home Secretary Theresa May - who had strongly defended her appointment - said she had accepted Mrs Woolf's resignation "with regret".
"I believe she would have carried out her duties with integrity, impartiality and to the highest standard," she said.
Mrs May - who is to make a Commons statement on Monday - said she would be meeting survivors' groups and consulting with relevant parliamentarians before appointing a successor.
Labour leader Ed Miliband said that Mrs May needed to explain why "basic background checks" which would have revealed Mrs Woolf's links with Lord Brittan were not carried out before she was appointed.
"It seems inexplicable, given what happened to the first head of the inquiry, that some basic questions were not asked of Fiona Woolf, before she was appointed, about her connections.
"Theresa May has some explaining to do. To lose one chair is a misfortune but to lose two is total carelessness on her part."
Mrs Woolf's links to Lord Brittan came under scrutiny because he is likely to be called to give evidence to the inquiry about his handling of child abuse allegations.
Documents published last night showed that a letter setting out Mrs Woolf's contacts with Lord Brittan and his wife was redrafted seven times, with guidance from Home Office officials, before being sent to Mrs May.
Mrs Woolf - who is the Lord Mayor of London - insisted that she had been "incredibly transparent" and that the Home Office was "just trying to be helpful".
The Home Affairs Committee chairman, Keith Vaz, said Mrs Woolf had been right to resign and called for an "open, robust, vigorous" process to appoint he successor.
"This has been chaotic," he said. "It is wrong for them (the Home Office) to have conducted this process in such way that two very distinguished women who are path finders in their fields should have had to resign from the inquiry."
Alison Millar, head of the abuse team at Leigh Day solicitors which represents some of the victims, also welcomed her decision to go.
"We are pleased that Fiona Woolf has stepped down and now the work begins for a proper inquiry which listens to the survivors and supports them in giving their evidence to an experienced panel," she said.
However, Mrs Woolf warned that it could be difficult to find a suitable replacement who was willing to take on the role in the face of intense media scrutiny.
"It is really going to be hard to find someone with no connections. A hermit?" she said.