LONDON—The head of Scotland Yard stepped down on Sunday and Rebekah Brooks—a close confidante of News Corp.'s top executive, Rupert Murdoch—was arrested as a convulsive phone-hacking scandal raced into the loftiest ranks of Britain's business and law-enforcement worlds.

The surprise resignation of Metropolitan Police Commissioner Paul Stephenson came amid a spreading onslaught of allegations that some members of his force were corrupt and had forged too-close ties with the discredited newspaper at the heart of the scandal,...