LONDON (Reuters) - 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 pounds ($27 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," interior minister Amber Rudd said in a statement.

A report in the Times newspaper on Thursday criticized 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 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 lawmakers, 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.

(Reporting by William James; Editing by Andrew Heavens and John Stonestreet)