The law firm Mishcon de Reya named the Daily Mail and London's Evening Standard as the subject of legal proceedings, adding that a suit will also be filed against The Sun.
Associated Newspapers, publishers of the Daily Mail and the Evening Standard, had no immediate response.
Mills McCartney had been vilified in the media and was now being stalked by photographers, the firm said. It alleged that other newspapers had also printed false statements but the three listed would be the focus of the lawsuit.
"She cannot sue — for now, at least — every single newspaper that has published false, damaging, and immensely upsetting statements about her. She should not thereby be taken to have accepted that these statements are true," the statement read.
The McCartney divorce has become the most sensational marital breakup since Prince Charles and Princess Diana parted ways a decade ago, sparking immense rivalry in the British press for the best scoop.
Last week, the Daily Mail splashed its front page with what appeared to be legal papers drafted by Mills McCartney's lawyers against the former Beatle that alleged drug use, drunkenness, callousness about his wife's amputated leg, indifference to her pain, and even an assault with a broken wine glass.
Mills McCartney's lawyers said British media claims that she has been offered a $56 million settlement by her husband are false and "the truth is that no settlement offer, in any amount, has been made."
"She is pursued everywhere she goes. She is stalked by press photographers, who congregate outside her home and chase after her in cars — regardless of her safety or the safety of her daughter," her lawyers said.
Mishcon de Reya issued a copy of a letter, apparently from The Mail on Sunday's investigations editor Dennis Rice, offering Heather's sister Fiona a "substantial sum" for information about the divorce.
It said the letter was hand-delivered and promised anonymity.
"It requires no imagination to conclude what kind of information was being sought from our client's closest confidante, nor why the assurance of confidentiality was believed to be necessary," the statement said. "We ask on behalf of our client for the media, as a matter of common decency, please now to show some restraint."