“It has been brewing for some time. Ever since the issue first arose I have been worrying about the negative perceptions and there has been a lot of negative comment and innuendo and that has got in the way as well.”
Mrs Woolf had come under mounting pressure over her links to Lord Brittan, whose actions while he was home secretary are expected to come under scrutiny in the investigation.
The former Cabinet minister denies failing to act on a dossier of paedophilia allegations he received while in office in the Eighties.
Ed Miliband, the Labour leader, said the case showed the Home Office had failed to carry out “basic background checks” on Mrs Woolf.
“Theresa May has some explaining to do. To lose one chair is a misfortune but to lose two is total carelessness on her part,” he said.
Keith Vaz, chairman of the home affairs select committee, said the final version of the letter appeared to show a “sense of great detachment” between Mrs Woolf and Lord Brittan than earlier drafts, and even facts had been “amended”.
Fiona Woolf: “There has been a lot of negative comment and innuendo.”
Before Mrs Woolf announced her resignation, lawyers and members of organisation which represent victims of child sex abuse met members of the inquiry team and said it was a “dead duck” while Mrs Woolf remained in post.
Peter Saunders, chief executive of the National Association for People Abused in Childhood, said: “I hope the Home Office now speak to people who should be at the heart of the investigation, the victims and survivors, before even thinking if foisting another name on us.
“We don’t want an inquiry doomed to failure. We would rather wait a week, month or year to get the right person. We don’t want another knee jerk appointment.”
Mr Vaz said: “This time, we must ensure that the process is open, transparent, robust and vigorous so that the nominee is able to assure all the stakeholders of their knowledge of the subject matter, their ability to devote sufficient time to it and their fitness for the job.”
Liz Davies, reader in child protection at London Metropolitan University who also attended the central London meeting with the inquiry team, said: “We were just the final straw that tipped the balance.
“We want an inquiry run by a high court judge who will compel evidence and documents to be seized. “We need a top legal representative in charge to force the truth to come out.”
Jane Collins, the Ukip MEP, said it had been an “absolute shambles”, adding: “Theresa May should look at herself and the performance of her department and do the decent thing and resign.”