Keith Vaz, the chairman of the Home Affairs Select Committee, tells the BBC that Mrs Woolf's resignation was "the right thing to do" given the "concerns of the victims".

Dominic Casciani, BBC Home Affairs Correspondent

tweets:, external Mrs Woolf, the current Lord Mayor of London, says that she has gone because she can't command the confidence of victims.

Home Secretary Theresa May says she regrets Mrs Woolf's resignation but insists the inquiry will continue with its work, adding that she will make a statement to Parliament on Monday "on its next steps".

tweets, external: "Asked who should chair the inquiry now: "it's going to be really hard to find someone with absolutely no connections. I mean, a hermit?""

Mrs Woolf told BBC Radio 5 Live's John Pienaar that it was clear "for some time" that victims did not have confidence in her, and that it was time to "get out of the way".

In response to the views expressed by the victims' groups, shadow home secretary Yvette Cooper said earlier it was "impossible to see" Fiona Woolf continuing as head of the inquiry.

Later, in an interview with the BBC's John Pienaar, Mrs Woolf, a lawyer and the current Lord Mayor of London, said: "If I don't command the victims' confidence I need to get out of the way."

Earlier, a meeting between victims' groups and officials from the inquiry took place in central London. They told Home Office officials they were "unanimous" in the view that she should resign.

Victims have been calling for her to step down because of her social links to ex-Home Secretary Lord Brittan.

Fiona Woolf has told the BBC she will step down as head of an inquiry into historic child sex abuse.

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