The under-fire Home Secretary was criticised by MPs for not consulting victims before the crossbench peer's appointment was made, given it had produced a possible conflict of interest because the establishment figure was set to probe claims about other establishment figures.
Also, the highly sensitive investigation is likely to look into the role of her late brother, Sir Michael Havers, the former Attorney General, who is reported to have tried in the 1980s to prevent the naming of an abuser in the UK Parliament by whistle-blowing MP Geoffrey Dickens.
Yesterday, the name of the ex-Scottish Conservative MP, the late Sir Nicholas Fairbairn, was drawn into the controversy after it was reported the former Solicitor General for Scotland visited the Elms Guest House in London, where youngsters from children's homes were allegedly abused. Sir Nicholas's daughter Charlotte was quoted as saying: "There's nothing I can say. He's been dead for 20 years."
Announcing her decision to step down, Lady Butler-Sloss acknowledged she "did not sufficiently consider" the difficulties her family connections might cause the inquiry.
In a statement, she explained: "This is a victim-orientated inquiry and those who wish to be heard must have confidence that the members of the panel will pay proper regard to their concerns and give appropriate advice to Government.
She added: "Having listened to the concerns of victim and survivor groups and the criticisms of MPs and the media, I have come to the conclusion that I should not chair this inquiry and have so informed the Home Secretary."
Keith Vaz, the Labour Chairman of the Commons Home Affairs Committee, said Lady Butler-Sloss's departure after just six days showed the inquiry process launched by Mrs May was becoming "shambolic".
He claimed the peer's departure was the latest indication of the Home Office "unravelling", following the resignation of the Home Secretary's special adviser in a briefing war with Education Secretary Michael Gove, crisis at the Passport Office and the admission that 114 files relating to allegations of historic child sex abuse had been lost.
But Mrs May hit back, saying: "I reject any suggestion that it is, in your words, unravelling."
She said she was "very sorry" Lady Butler-Sloss had stepped down but added: "I continue to believe that she would have done an excellent job...I do not regret the decision I made."
Mr Vaz pointed out that the only person who had defended the former judge's appointment was her nephew, the actor Nigel Havers.
The Committee Chairman urged Ms May to consult more widely, including with victims' groups, before appointing a replacement chair, whom, he suggested would have to have "the virtues of Mother Teresa".
The Home Secretary said she could not provide a timetable for the appointment of a new inquiry chairman but promised: "We will not be hanging around."
Campaigning MP Simon Danczuk, who triggered the launch of the inquiry by questioning the handling of Mr Dickens's allegations by then Home Secretary Lord Brittan, welcomed Lady Butler-Sloss's decision to step aside and said the "priority now is to find a strong and independent person to chair the inquiry."
Author Alex Wheatle, who was abused at a children's home in the late 1960s, said victims had to be "100% sure they will be treated fairly", adding: "For any people coming forward, they must have the utmost confidence in whoever chairs that inquiry."