Image copyright PA Image caption Prof Alexis Jay became the inquiry's fourth chairwoman in August

The chair of the independent inquiry into child sex abuse has vowed to continue after a victims' group quit and called for her to be replaced.

In the Times, Prof Alexis Jay wrote: "I have fought for this... I don't intend to stop fighting for it now."

The Shirley Oaks Survivors Association, for 600 victims who lived in children's homes in London, said it did not have confidence in the inquiry's leadership.

But Home Secretary Amber Rudd has backed Prof Jay's leadership.

Prof Jay, who is the fourth chair of the inquiry following earlier resignations, wrote that she was "genuinely saddened" by the group's decision to withdraw "but our work continues".

'Dark institutional failings'

She wrote: "I have fought for this inquiry - for its independence, its reputation and its vital capacity to right a terrible wrong - since it opened, and I don't intend to stop fighting for it now.

"There are some people who would like to see us fail because it suits their agenda to not want dark institutional failings brought into the light.

"But shine that light we will, because there are many, many people in this country who spend every waking minute of every day living with the damage and the pain caused by child sexual abuse."

The treatment of children in care in Lambeth, south London, from the 1950s onwards is one of 13 areas the Independent Inquiry into Child Sexual Abuse (IICSA) is due to look at.

It will investigate the claim that a large paedophile network infiltrated children's homes in the area, run by Lambeth Council, with the Shirley Oaks group due to have been a "core participant" in the process.

On Friday the group called the inquiry a "stage-managed event" and an "unpalatable circus" which had "lurched from crisis to crisis".

Image caption Dru Sharpling said Prof Alexis Jay was "one of the few people qualified" to lead the inquiry

Raymond Stevenson, who has spoken about being physically abused during his time at the Shirley Oaks home in the 1970s, said: "The inquiry needs to sort itself out. They need to get rid of Alexis Jay, who's been parachuted in by the Home Office. She's not the right person."

Labour MP Chuka Umunna called for a new head, but inquiry panel member Dru Sharpling defended chairwoman Prof Jay as being "qualified for the job."

Prof Jay wrote that the Shirley Oaks Survivors Association "condemns me for having been a social worker and asks how this inquiry can truly be independent.

"But anyone who knows me, has worked with me or is familiar with my record at other inquiries knows I have vigorously scrutinised the work of social workers and all other agencies."

The inquiry said in a statement: "Our investigation will continue and will examine the scale and nature of the abuse that may have taken place under the care of Lambeth Council with pace, confidence and clarity."

The inquiry has been beset by difficulties since it was set up in July 2014 to investigate allegations made against local authorities, religious organisations, the armed forces and public and private institutions in England and Wales, as well as people in the public eye.

Three chairwomen - former president of the High Court Family Division Baroness Butler-Sloss, her replacement, leading lawyer Dame Fiona Woolf, and Justice Goddard, a New Zealand high court judge - have already stood down before Prof Jay took charge.

A number of senior lawyers on the inquiry have also quit - the most recent of which was Aileen McColgan, who resigned on Wednesday amid concerns about the inquiry's leadership.