Speaking today at the Lord Leveson Inquiry, Church said that she was made an offer to sing at the wedding of Rupert Murdoch and Wendi Deng in 1999 on the billionaire's yacht in New York.
The singer claimed that her manager advised her to do the gig as a favour instead of asking for a £100,000 fee, as it would involve her getting positive coverage in Murdoch-owned newspapers.
She said she was advised that Murdoch was a "very, very powerful man" and that she could do with the favourable coverage as she was at that time in the early stages of her career.
News International, Murdoch's UK newspaper group, strongly denies ever making the offer.
Church also today discussed the "psychological grinder" that she has been put through by the newspapers, including alleged phone hacking, paparazzi attention and harassment.
The singer said that media interest in her started from the age of 11 with just "kid gloves" as she didn't have "any skeletons" at that age. But that started to change after she was around 14, when it became more intrusive and negative.
She claimed that she was regularly followed by reporters and photographers, and described a "kind of shadow network where everyone is infiltrated", including hotel concierges and airline workers.
Church said that she hasn't been on a holiday since she was 16 where she wasn't followed by at least one reporter or photographer.
The singer discussed the moment when The Sun ran a countdown clock on its website, which allegedly inferred that it was counting down to her passing the age of consent at 16 for legally having sex.
She said that the clock was "a little bizarre" and "just horrible", adding: "I was a 10-year-old girl and [I was] just really uncomfortable with it in general."
Discussing the intrusion in her life over the years, Church said that she had to "endure the worst excesses of the press" between the ages of 16 and 20, when there would be photographers outside her house five out of seven days of the week. She said that this would rise to six or eight photographers if a big story had broken, which was "really intense".
At one point, she said that her manager found that someone had cut holes in a bush near the entrance to her home and installed a camera there to track her movements. She never found out who was responsible for that.
As she frequently attended events, she said that she had to endure photographers trying to take pictures up her skirt or down her top, or trying to capture unflattering images, such as exposing "cellulite or whatever".
Earlier in the year, police informed Church that her phone may have been hacked by Glenn Mulcaire, the private investigator jailed for phone hacking on behalf of the News of the World.
Officers showed her passwords and pin numbers of "lots of people" in her life, along with "quite substantial" information covering the period from 2003 to 2006. The earliest indication was that her phone had been hacked when she was just 17.
"Even though we as a family felt that the press has used some dreadful tactics to get a story, it was still quite bemusing [to hear about the hacking]," she said.
"When I was younger I had quite a big group of girlfriends, but more and more I was wondering how this stuff came out, [and so] I was cutting people out as I tried to get a closer group."
After realising that the information may have leaked out because of her phone had been hacked, Church said that she felt guilty about blaming people for what was not their fault.
She further recalled blaming her mother for leaking news about her daughter Ruby's birth two days after it had happened, which also occurred because her voicemails had been intercepted.
An earlier article, entitled 'Church sober shock', published in The Sun reported that the singer had stopped drinking alcohol and had put on weight, suggesting that she was pregnant.
Church feels that the story was down to evidence hacked from her phone, or her doctor's phone, but she admitted that she had no evidence to support that. She submitted a complaint with the Press Complaints Committee about the story, which was upheld.
She said: "Surely it is any woman's right to tell her family and friends when she is pregnant... but they took that away from me.
"The PCC complaint was upheld, but what does that mean? There was a small retraction, but I did not think that would deter anyone else from doing this again."
Church said that newspaper coverage of her parents' lives has been "particularly painful", including a News of the World article alleging that her father had an affair, with the headline "Church's three in a bed cocaine shock".
She said that the article was "just totally sensationalised" and had no public interest apart from "to sell papers". She said that the story had a "massive, massive impact" on her family's life, including her mother's attempted suicide being "at least in part" because she knew the story was coming out.
Another damaging article was actually not published by a tabloid, but by The Sunday Times as part of an interview Church gave aged 15 after the September 11, 2001 attacks.
She had felt that the interview went well, but was "totally shell shocked" that the published version of the story suggested that she was denigrating the 9/11 New York firefighters.
Church claims that she actually said that the firefighters presenting a 'Best Soap' award was in "bad taste" against their heroism, but she said that was not the angle reflected by the paper.
After the story was picked up by the New York Post, Church was subject to a "massive backlash" against her in America, leading her to need bodyguards on the street.
Concluding her evidence, Church said: "I feel strangely strong because I've survived it all and I don't know how because at times it really messes with your mind.
"In a way I think it's made me stronger but professionally because I've been made a caricature for so long and that really isn't me, the person I am or the way I live my life.
"I think that has had a massive impact on my career. As an artist and a singer, I find it really hard to get taken seriously as my credibility has been blown to bits by this publicity."
Church added that "it's almost like they put you in the psychological grinder and they test your strength", but admitted she "hasn't got a clue" how to regulate the press in future.
Leveson Inquiry coverage roundup:
> JK Rowling criticises 'threatening' press treatment
> Harry Potter newspaper articles criticised by JK Rowling
> Sienna Miller 'baffled and intimidated' by press intrusion
> Madeleine McCann parents Kate and Gerry 'violated' by press intrusion
> Phone hacking goes beyond News of the World, says lawyer
> Steve Coogan: Newspaper industry is like the mafia
> Phone hacking made Dowler family think Milly was alive
> Hugh Grant suspects Mail On Sunday of phone hacking