LONDON — In the growing storm surrounding the BBC’s handling of an investigation of child sexual abuse accusations against one of its longtime television hosts, the network’s current director general has largely stood as the public face of the revered institution, enduring heated inquiries from Parliament and the stinging outrage of viewers.

But with details of the case of Jimmy Savile spilling out day by day, questions are increasingly being directed at a wider range of executives, particularly Mark Thompson, who until recently was the BBC’s director general and is the incoming president and chief executive of The New York Times.

Thompson, the BBC’s chief from 2004 to September 2012, was not in charge during the years when Savile is now said to have engaged in widespread pedophilia. But he was when Savile died at age 84 in October 2011 and two branches of the network set off in very different directions to examine the life of the eccentric host.

Precisely why an investigation by the BBC program “Newsnight” into allegations of Savile’s pedophilia was killed while a package of Christmastime tributes to the host were broadcast was at the heart of a parliamentary hearing Tuesday that featured an uncomfortable and apologetic George Entwistle, the current director general.

In the wake of that hearing, Roger Gale, a former BBC producer and current member of Parliament, asked in a statement why Entwistle’s predecessors were not being pressed for answers, “most particularly the man who was in the hot seat when the ‘Newsnight’ decision was taken, Mark Thompson?” Gale’s statement said Thompson was well-paid “to, apparently, not know what was going on under his own roof.”

Since the scandal broke, Thompson has said he knew nothing about the “Newsnight” investigation, had no role in canceling it and had heard none of the suspicions about Savile.