In November, Blair's former press secretary Alastair Campbell told the Leveson Inquiry he had wrongly suspected Cherie Blair's friend Carole Caplin of tipping off newspapers about her.
Close to 100 alleged phone-hacking victims are considering formal High Court claims against News International, and Church's trial is still on course to provide a high-profile conclusion to the first wave of cases.
Despite signals that Rupert Murdoch's UK subsidiary had made a substantial offer that was close to being accepted by the Welsh singer and her family, differences between the two sides have not been resolved.
Church's phone-hacking battle, scheduled to begin on Monday, is the last one standing out of six test cases expected to provide the High Court with a framework that would be used for other claims against NI.
The reasons for the remaining gulf between NI and Church are unclear.
However, in the recent pre-trial review before Justice Vos, NI's senior counsel, Michael Silverleaf, QC, made it clear that the business affairs of the singer's family, and the mental health of her mother, Maria, would be a key issue in the trial.
This indicated that NI's defence against Church will go beyond her own personal life.
The intention to focus on the intimate details of her parents' private life may have hardened the resolve of the singer to seek punitive damages in court for the distress she says was caused to her family by the News of the World. Independent
