The head of a public inquiry into decades of child sex abuse in Britain resigned on Thursday, the investigation's third leader to quit in the last two years.

The inquiry, which will last at least five years and is expected to cost about £18 million, was set up in July 2014 after a series of child sex abuse scandals dating back to the 1970s, some involving celebrities and politicians.

On Thursday its chairwoman, New Zealand High Court Judge Lowell Goddard, quit without publicly explaining her decision.

Her appointment was seen as an attempt to give the inquiry a credible head without links to the British political establishment after her two predecessors resigned amid criticism over conflicts of interest.

"Dame Lowell Goddard wrote to me today to offer her resignation as Chair of the Independent Inquiry into Child Sexual Abuse and I have accepted," Home Secretary Amber Rudd said in a statement.

Goddard followed her brief resignation with a statement in which she said accepting the role as inquiry chair 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."

Phil Johnson, spokesman for the Minister & Clergy Sexual Abuse Survivors group, told the Telegraph: "This latest resignation is deeply disappointing and worrying and I fear for the future of the whole inquiry at this moment.

"The inquiry is already massively behind schedule.

"I am very surprised she has resigned. I don't know what the reasons are but I can't imagine it's the criticism in The Telegraph and the Times. It must go deeper than that.

"I am shocked and deeply concerned about the future of the inquiry. She was the third chair. This means pressing the reset button again and I don't know what the public appetite is for that. It is in danger of looking like a farce. We do need an inquiry to get to the truth and this does not help."

A report in the Times newspaper on Thursday criticised Goddard, saying she had spent three months of her first year in the role either on holiday or overseas. Goddard did not mention the report in her 32-word resignation letter.

Abuse victims have accused politicians as well as the Roman Catholic and Anglican Churches, councils and schools of failing to deal with allegations.

In a number of cases, they said institutions had actively covered up cases at the behest of powerful establishment figures including senior MPs, spies and police officers

"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 and a new chair will be appointed," Rudd said.

Additional reporting by Reuters.