The inquiry into child sexual abuse will continue "without delay" and in the absence of a new chair, Home Secretary Amber Rudd has said, after the resignation of Dame Lowell Goddard.
Ms Rudd thanked the New Zealand high court judge for her contribution to setting up the inquiry.
The investigation was set up in July 2014 to examine claims made against public and private institutions.
Justice Goddard was selected after two previous chairwomen quit.
In her resignation letter, Justice Goddard said conducting such a widespread inquiry was "not an easy task" but "compounding the many difficulties was its legacy of failure which has been very hard to shake off".
Ms Rudd said in a statement: "I want to assure everyone with an interest in the inquiry, particularly victims and survivors, that the work of the inquiry will continue without delay...
"I would like to thank Dame Lowell Goddard for the contribution she has made in setting up the inquiry so that it may continue to go about its vital work."
BBC home affairs correspondent Tom Symonds described the resignation as a "crisis" for the inquiry.
It came on the same day the Times reported that Justice Goddard had spent more than 70 days working abroad or on holiday during her time in charge.
An inquiry spokesman told the newspaper she had spent 44 working days in New Zealand and Australia on inquiry business in its first financial year and that she was entitled to 30 days' annual leave.
Peter Saunders, from the National Association of People Abused in Childhood and a member of the inquiry's victims and survivors panel, said: "I personally wonder whether or not we actually need a chair; maybe it is too much of a burden for one person...
"Everything is finally taking off and I don't think we should be too distracted by the unfortunate departure of just one person."
'Gains for victims'
In a statement, Justice Goddard 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 said she took on the role because of her "relevant experience and track record in the area" but it was "an incredibly difficult step to take, as it meant 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."
The inquiry was set up 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.
It had a budget of £17.9m in its first year, funded by the Home Office, with staffing-related costs accounting for 41% of the total.
Justice Goddard was receiving a salary of £360,000, an annual rental allowance of £110,000 and £12,000 a year to cover utilities, while panel members were each receiving £565 a day.
Who is Justice Goddard?
- Born in Auckland, New Zealand
- Third person to be appointed chair of the inquiry since it was set up in 2015
- Serving judge of the High Court of New Zealand and UN committee member with experience of working with victims of sexual assault
- In 2007, she was appointed chairwoman of New Zealand's Independent Police Conduct Authority
The original chairwoman, Baroness Butler-Sloss, stood down after just a week following questions over the role played by her late brother, Lord Havers, who was attorney general in the 1980s.
Her replacement Dame Fiona Woolf resigned following questions over her links to establishment figures.
The inquiry's preliminary hearings began in March at the Royal Courts of Justice in London. A panel of advisers had also been selected and the inquiry's terms of reference agreed.
In February 2017 there will be two weeks of hearings relating to the sexual abuse of British child migrants, who moved to parts of the British Empire and Commonwealth between 1920 and 1970.
Public hearings into allegations of abuse relating to Lord Janner are due to start on 7 March and are expected to finish by the end of May.
The Labour peer, who died in December, was accused of sex offences against children - which his family deny.
Abuse inquiry: How we got here
7 July 2014 - government announces independent inquiry into the way public bodies investigated and handled child sex abuse claims. Baroness Butler-Sloss chosen as head
9 July - Baroness Butler-Sloss faces calls to quit because her late brother, Sir Michael Havers, was attorney general in the 1980s
14 July - she stands down, saying she is "not the right person" for the job
5 September - Lord Mayor of London Fiona Woolf named the new head of the inquiry
11 October - Mrs Woolf discloses she had five dinners with Lord Brittan from 2008-12
22 October - abuse victim launches legal challenge against Mrs Woolf leading the inquiry, amid growing calls for her resignation
4 February 2015 - Justice Lowell Goddard, a serving judge of the High Court of New Zealand, announced as the new head of the inquiry
13 July - Dame Lowell's pay is revealed as more than £480,000 a year
November - inquiry begins hearing directly from victims and survivors
4 August 2016 - Dame Lowell writes to Home Secretary Amber Rudd to resign from her post