LONDON (Reuters) - Britain appointed a new head to lead a national inquiry into decades of child sex abuse on Thursday, naming social care expert Alexis Jay to lead an investigation that has been dogged by leadership problems.

The inquiry was set up in July 2014 after a series of child sex abuse scandals dating back to the 1970s, some involving celebrities and politicians.

Jay, who led a separate 2014 investigation into child sexual abuse in the northern English town of Rotherham, becomes the fourth person to lead the wide-ranging inquiry after its former chair, New Zealand High Court Judge Lowell Goddard, quit last week.

"Together with my fellow panel members, we will fearlessly examine institutional failures, past and present, and make recommendations so that the children of England and Wales are better protected now and in the future," Jay said in a statement.

Described by the government as a "a child protection expert with over 30 years' experience", Jay had already been working as a member of the panel investigating allegations from victims who say politicians, the Catholic and Anglican Churches, councils and schools have failed to deal with abuse.

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

Two other chairwomen previously quit the inquiry amid criticism over conflicts of interest relating to their ties to the political establishment.

"Let there be no doubt; our commitment to this inquiry is undiminished," interior minister Amber Rudd said, announcing the appointment.

"We owe it to victims and survivors to confront the appalling reality of how children were let down by the very people who were charged to protect them and to learn from the mistakes of the past."

(Reporting by William James; editing by Stephen Addison)