LONDON — Britain’s Supreme Court took a step toward exposing the names at the heart of the nation’s phone hacking scandal Wednesday, ruling that a private investigator convicted of eavesdropping for a Rupert Murdoch-owned tabloid must reveal who told him to do it.

Meanwhile, a police investigation into press wrongdoing triggered by the hacking revelations expanded beyond Murdoch’s media empire with the arrest of a former reporter from the rival Mirror group.

Private eye Glenn Mulcaire was jailed briefly in 2007 for hacking the voice-mail messages of royal aides on behalf of the now-defunct News of the World. Hacking victims suing Murdoch’s News International want Mulcaire to provide evidence for their cases by identifying the editor who told him to hack the phones. Mulcaire attempted to refuse to name names under laws that prevent self-incrimination, but five judges from the high court rejected that argument. The judges did not set a deadline for Mulcaire to comply, but Phillips’ lawyer said he expected him to reveal the name within the next three weeks.

More than 40 people have been arrested and several have been charged in the scandal.