The nominal sum was set out in court documents which formally confirm the newspaper has accepted defeat.

The Mail on Sunday published a handwritten letter the duchess sent to her father Thomas Markle in 2018.

The media company will also pay an unspecified sum for a separate case of infringing her copyright.

Associated Newspapers previously indicated it was considering a further appeal to the Supreme Court, but the company has now accepted defeat in the long-running case.

Last February, the High Court had ruled against the newspaper group on the issue of privacy and copyright – saying the issues in the case were so clear cut that there was no need for a full hearing.

Associated Newspapers was refused permission to appeal against the decision but went to the Court of Appeal in an attempt to get the original ruling overturned.

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However, in December, the Court of Appeal rejected Associated Newspapers’ attempt to have a trial.

Judges at the appeal said it was hard to see what evidence at a trial would have altered the situation.

They added: “The judge had correctly decided that, whilst it might have been proportionate to publish a very small part of the letter… it was not necessary to publish half the contents of the letter.”

A spokesman for Associated Newspapers said at the time: “It is our strong view that judgment should be given only on the basis of evidence tested at trial, and not on a summary basis in a heavily contested case.”

In her own statement issued after the ruling, the duchess urged people to be “brave enough to reshape a tabloid industry that… profits from the lies and pain that they create”.

Associated Newspapers will also pay a confidential sum for copyright infringement, while the Mail on Sunday also faces having to cover a substantial part of Meghan’s legal costs, which could be more than £1m.

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Media lawyer Mark Stephens told the Guardian the nominal £1 settlement suggested a weakness in the privacy aspect of the duchess’s case.

“Normally for that kind of invasion of privacy you would expect £75,000 to £125,000,” he said. “It does show that the curation of her reputation was an area where she had effectively invaded her own privacy.”

However, libel lawyer David Hooper told The Daily Beast: “Accepting the £1 will likely have avoided a tremendous argument about the extent of the damage she suffered.

“She just wanted to establish a principle and get her legal costs paid, although she may well still be a half a million pounds out of pocket as a result of this process.”