LONDON—The criminal trial of former News Corpexecutive Rebekah Brooks and several of the company's former employees involved in an alleged phone-hacking scandal starts here Monday, kicking off a courtroom drama that could further embarrass both the media giant and the British government.

Prosecutors have charged Ms. Brooks, a onetime protégé of News Corp Executive Chairman Rupert Murdoch, with a variety of offenses, including conspiring to illegally intercept mobile-phone voice-mail messages—known widely as phone hacking. She...