Policeman Alan Tierney admitted selling information to The Sun newspaper about arrests including the case involving Rolling Stones guitarist Ronnie Wood. Prison officer Richard Trunkfield admitted providing the tabloid with information about a prominent prisoner.
They were arrested as part of the Operation Elveden investigation into allegations that newspapers were paying police and other officials for information.
The bribery inquiry is running alongside investigations into phone hacking and computer hacking sparked by revelations that reporters at Murdoch's now-shuttered News of the World routinely intercepted voicemails of those in the public eye.
Almost 100 people have been arrested and about 20 charged over the scandal, including journalists, police officers, former Murdoch executive Rebekah Brooks and Andy Coulson, Prime Minister David Cameron's former communications chief.
Brooks, 44, and Coulson, 45, both appeared in court Friday for short hearings. The cases were adjourned until next month.
So far, one person has been convicted as a result of the investigations—a senior detective found guilty earlier this year of trying to pass police information to the News of the World.