The Mail On Sunday's publisher will begin a Court of Appeal challenge in its ongoing legal battle with the Duchess of Sussex over a "personal and private" letter to her estranged father.
Meghan, 40, sued Associated Newspapers Limited (ANL), also the publisher of MailOnline, over a series of articles which reproduced parts of a "personal and private" letter to Mr Markle, 77, in August 2018.
She claimed the five articles, published in print and online in February 2019, misused her private information, infringed her copyright and breached the Data Protection Act.
Meghan won her case earlier this year, after Lord Justice Warby ruled that ANL's publication of Meghan's letter to her father was "manifestly excessive and hence unlawful".
Giving a ruling in February, the judge said: "It was, in short, a personal and private letter.
"The majority of what was published was about the claimant's own behaviour, her feelings of anguish about her father's behaviour, as she saw it, and the resulting rift between them.
"These are inherently private and personal matters."
The judge said "the only tenable justification for any such interference was to correct some inaccuracies about the letter", contained in an article in People magazine, published days before ANL's five articles, which featured an interview with five friends of Meghan.
But Lord Justice Warby added: "The inescapable conclusion is that, save to the very limited extent I have identified, the disclosures made were not a necessary or proportionate means of serving that purpose.
"For the most part they did not serve that purpose at all.
"Taken as a whole, the disclosures were manifestly excessive and hence unlawful."
In March, the publisher was ordered to print a statement on the front page of the Mail On Sunday and a notice on page three of the paper stating it "infringed her copyright" by publishing parts of the letter to Mr Markle.
But the front-page statement about Meghan's victory has not been published yet as it is on hold pending the outcome of the appeal.
In a further ruling on copyright issues in May, the judge said ANL must "use its best endeavours" to locate any copies of the draft of Meghan's letter to Mr Markle and provide them to the publisher's lawyers, who will destroy them "at the end of the action, so long as the claimant ultimately succeeds".
The judge concluded he could make the rulings without the need for a full trial of the issues involved.
The publisher's appeal is being heard by Sir Geoffrey Vos, Dame Victoria Sharp and Lord Justice Bean over three days, and the judges are expected to give their ruling at a later date.
The hearing starts at 10.30am on Tuesday and will continue until Thursday.