The High Court heard that the singer's phone was hacked when she was 16 years old.
Reports are that the Welsh singer, now 26, has said that 33 articles in the now defunct News of the World tabloid were a result of journalists illegally hacking into her family's voice mails.
After agreeing to a settlement, Church told the BBC that she and her family wanted to find those responsible and have them explain their actions.
Money could never mend the damage that was done, Church said, adding that her portion of the settlement will be used to protect the privacy of herself and her children.
According to The Associated Press, News International, which is a division of Murdoch's News Corp., has tried to keep the phone hacking cases from going to trial and has launched a compensation program. That program is overseen by a former judge and has paid out millions in out-of-court settlements for about 60 cases, The AP reported.
What I have discovered as the litigation has gone on has sickened and disgusted me, Church told the BBC. Nothing was deemed off limits by those who pursued me and my family just to make money for an international news corporation. Of course, I was a teenager at the time and my parents were not in the public eye. They just happened to have a well-known daughter. Whatever I have had to go through they have suffered as well.
Church also told the BBC that she was harassed, put under surveillance and that her mother was bullied into revealing a private medical condition for no reason.
Someone in a newspaper thought that was OK, Church said. How can that be in any right thinking society? I wanted to bring the individuals responsible to court and make them explain why they did this to me and my family.
She added that despite the apology from the newspaper in court, the organization was prepared to go to any lengths so that she doesn't expose their behaviour. Church claimed that documents were deliberately destroyed over the years and that the newspaper tried to make the investigation into their illegal activity into an interrogation of her mother's medical condition.
It seems they've learned nothing, she said. And I would have learned nothing more from an actual trial since it was clear that no one from News International was prepared to take the stand to explain their actions. In my opinion, they are not truly sorry. Only sorry they got caught.