LONDON — On the fourth day of the phone-hacking trial in London, the jury was told that Andy Coulson, the former editor of Rupert Murdoch’s News of the World newspaper, had authorized a payment to a police officer to steal a directory containing the phone numbers of staff working for the British royal family.

According to Andrew Edis, the prosecutor in the trial, the paper’s royal editor, Clive Goodman, sent an email to Coulson in 2003 asking for approval for a payment of £1,000 ($1,590) to the officer to steal the directory.

In an email to Coulson, Goodman complained that Stuart Kuttner, the paper’s managing editor, was reluctant to authorize the payment.

“I’m not criticizing Stuart at all, but these people will not be paid in anything other than cash because if they’re discovered selling stuff to us they end up on criminal charges, as could we,” Goodman’s email stated.

Coulson reply was, “This is fine.”

Coulson and Goodman deny the allegation.

The jury also heard that a private investigator, Glenn Mulcaire, illegally listened to a voicemail from Prince Harry to his aide, Jamie Lowther-Pinkerton, asking for help with an essay he was writing at Sandhurst military academy. Mulcaire did so on behalf of Goodman, the court was told.

Mulcaire and Goodman already have been convicted of phone hacking.