Video report by ITV News Political Correspondent Libby Wiener

The third chairman of a troubled inquiry into institutional child sex abuse has been asked to explain herself to MPs after her shock resignation.

The inquiry was thrown into fresh turmoil after its New Zealand high court judge Dame Lowell Goddard resigned as chairman.

She claimed the inquiry had struggled to shake off its "legacy of failure" and called the job a "struggle".

Keith Vaz MP has written to Goddard to ask her to appear before the Home Affairs Select Committee to explain her "extremely disappointing" resignation.

Vaz, chairman of the committee, told Sky News: "She is someone with impeccable credentials, so this is a big shock that she chooses to resign now.

"I think what's really important is that we find out the reasons why she has decided to take this course of action."

"What she has to say is extremely pertinent, and I don't really think a resignation letter or a statement is enough," Vaz said.

The inquiry, which is unprecedented in scale, was set up in March 2015 to investigate historical child sex abuse allegations against local authorities, religious organisations, the armed forces and other public and private institutions.

Home Secretary Amber Rudd, who accepted Dame Lowell's resignation on Thursday, insisted the new inquiry would "continue without delay" and a new chairman would be found.

But survivors told ITV News they felt "let down" and "bewildered" by yet another resignation.

Dame Lowell, 67, was appointed in February 2015 to after two previous choices stood down over concerns about their links to establishment figures.

Then Home Secretary Theresa May's first choice Baroness Butler-Sloss stood down in July 2014 as her brother was attorney general in the 1980s.

Her replacement, Lord Mayor of London Fiona Woolf, quit in October the same year following concerns over her links to former Home Secretary Leon Brittan.

Dame Lowell - who received a pay packet worth more than £480,000 a year for the role - resigned on the same day as the Times reported that she had spent more than 70 days working abroad or on holiday during her time in charge.

An inquiry spokesman said she had spent 44 days in New Zealand and Australia on inquiry business and was entitled to 30 days' annual leave.

Butler-Sloss quit in July 2014. Credit: ITV News

Fiona Woolf also did not last long in the job. Credit: ITV News

The estimated cost of the inquiry and its predicted finish date Credit: ITV News

Dr Phil Frampton, from a survivors campaign group, said the appointment "always was a high-risk appointment by Theresa May".

"She came from a country 10,000 miles away with no real knowledge of the British system."

Peter Saunders, from the National Association of People Abused in Childhood, said he was "absolutely certain" the inquiry would continue and be effective.

Ray Stevenson, who experienced abuse, told ITV News: "It's just another abuse. When you are persuaded to come forward and announce the abuse that's happened to you...and then to be let down this way.

"You have to look at who appointed Goddard - she was never the right person obviously."

Another survivor, Phil Johnson told ITV News he was "bewildered" and "betrayed" at the third resignation.

Peter Garsden, a lawyer specialising in representing child abuse victims, said that the inquiry will need a "very special and determined person to see it through to the end".

In her resignation letter to the home secretary, the judge said she was "confident there have been achievements and some very real gains for victims and survivors of institutional child sexual abuse in getting their voices heard".

She also spoke of the difficulty of "relinquishing my career in New Zealand and leaving behind my beloved family".

She added: "The conduct of any public inquiry is not an easy task, let alone one of the magnitude of this. Compounding the many difficulties was its legacy of failure which has been very hard to shake off and with hindsight it would have been better to have started completely afresh."

Victims have reacted with dismay at the latest setback. Credit: ITV News

Accepting Dame Lowell's resignation, Mrs Rudd wrote: "I know how personally committed you have been to ensuring that the inquiry is a success for those at its heart: the survivors and the victims.

"You have consistently demonstrated your desire to leave no stone unturned in order that the voices of those victims might be heard.

"It is a testament to your commitment that you have taken the difficult decision to stand down now, having set the inquiry firmly on course, and allow someone else to lead it through to the end. With regret, I agree that this the right decision."

ITV News Political Correspondent Libby Wiener said that the third resignation of the child abuse inquiry chairman is "embarrassing" for the government.

The appointment of Dame Lowell Goddard by Theresa May, as someone independent from the British establishment, means that new Home Secretary Amber Rudd is "back at square one" to find a replacement.