The singer Charlotte Church was encouraged by her advisers to accept an offer from Rupert Murdoch to exchange favourable coverage in his newspapers for an agreement to sing at his wedding, she told the Leveson inquiry on Monday.

Church's evidence – and that of the broadcaster Anne Diamond – offered a remarkable insight into the modus operandi of the world's most powerful media mogul when the two spoke at the inquiry into press ethics.

Diamond claimed in her evidence that she had been targeted by the Murdoch press after she challenged him over his papers' treatment of celebrities including Princess Diana and Elton John during an encounter in the 1980s.

Church said she was offered £100,000 to sing at Murdoch's wedding to Wendi Deng in 1999, when she was 13. She claimed she was told if she waived the fee she would be looked upon favourably by Murdoch's papers. She said: "I remember being told that Rupert Murdoch had asked me to sing at his wedding to Wendi Deng and it would take place at his yacht in New York". Murdoch married Deng, his third wife, on board his boat Morning Glory in a small private service in New York harbour.

"I remember being told of the offer of the favour – to get good press – and I also remember being 13 and thinking why would anyone take a favour over £100,000?"

Murdoch's News Corp, whose UK papers include the Sun and the Times, deny any such offer was made, but Church said she recalled detailed negotiations taking place with Murdoch, who is chief executive and chairman of the company. "He had specifically asked for me to sing Pie Jesu," Church said, adding that she had responded by questioning whether a funeral requiem was suitable for a wedding.

"The correspondence went back and forth and he said he didn't care if it was a funeral song, he liked that song, he wanted me to sing it, so I did," Church said.

Her evidence suggested the Sun failed to honour the bargain, if such a deal had been agreed. She criticised a feature on the paper's website, which carried a clock counting down to Church's 16th birthday alongside "sexual innuendo". "I was a 16-year-old girl and I was just really uncomfortable with it," she said.

The Sun also revealed she was pregnant before she had told her parents. "My parents were really upset that, you know, I hadn't told them first," Church said. "Surely it's any woman's right to tell her family or her loved ones when she feels the time is appropriate that she's pregnant?"

Church also told of her distress after the News of the World, which was closed in July, ran a front page story under the headline: "Church's three in a bed cocaine shock". The report said: "Superstar Charlotte Church's mum tried to kill herself because her husband is a love rat hooked on cocaine and three in a bed orgies."

Church said: "I just really hated the fact that my parents, who had never been in this industry, apart from looking after me, were being exposed and vilified in this fashion."

She claimed the paper was aware her mother had been seeking medical help: "They knew how vulnerable she was and still published this story."

Diamond, who described how she was "catapulted" to fame in 1983 after joining ITV breakfast franchise TV-am, claimed she was targeted by Murdoch's tabloids after chastising him for their behaviour.

"I had put to Rupert Murdoch … somewhat precociously perhaps … that his newspapers seemed to be intent on ruining peoples lives." Diamond added she had been referring to the papers' coverage of Princess Diana and Elton John.

She said Murdoch's former butler, Philip Townsend, told a Channel 4 documentary team earlier this year that conversation had been relayed to senior executives at Murdoch's British newspapers. "From that moment onwards there were consistent negative stories about me in Mr Murdoch's newspapers," Diamond claimed.

She said the Sun had run a front page story in 1987 about a car crash she was involved in seven years earlier in which a man had died, under the headline: "Anne Diamond killed my father". She was cleared of any wrongdoing following an investigation.

She complained to the Press Council, the Press Complaints Commission's forerunner, which regulated newspapers at the time, and her complaint was upheld.

Diamond also gave harrowing evidence about her treatment by the press at the time of the birth of her first child. She was told while in labour that a Sun reporter had been found at the hospital posing as a doctor. She had to be smuggled out of the building in a laundry van and returned to her flat via a neighbouring building.

Diamond also said she and her then husband, Mike Hollingsworth, wrote to every newspaper editor in 1991 when their baby son Sebastian died, to ask to be left alone to grieve at his funeral.

A single photographer took a photo of their baby's coffin with a long-lens camera and the Sun phoned to say they would be using the image despite her partner's objections. The paper subsequently asked her to take part in a campaign to raise awareness of cot death.

Diamond said she felt "emotionally blackmailed by the people who I felt had just trampled all over our dignity and all over our child's grave". But she eventually agreed to take part in the paper's campaign despite that, she added.

Diamond and Church were both critical of press self-regulation. Church said in her witness statement that small corrections published in newspapers "were hardly likely to deter" further bad behaviour.

Diamond compared the PCC unfavourably with regulation of broadcasters by Ofcom, which she said did not prevent excellent investigative journalism.