Mark Thompson, the former director-general of the British Broadcasting Corp., started work on Monday as the chief executive of The New York Times Co. Thompson started his new job amid a widening scandal at his former employer.

In recent months, Thompson has faced questions over a decision by the BBC’s “Newsnight” program last December to shelve an investigation into child sexual-abuse allegations against renowned BBC children’s television host Jimmy Savile. That decision was made while Thompson was still in charge of the company.