Hollywood star Johnny Depp has been refused permission to appeal against a UK court decision that upheld claims made by The Sun newspaper that branded him a "wife beater".

The 57-year-old "Pirates of the Caribbean" actor was also ordered to pay the newspaper's £628,000 (€705,000) legal costs, court documents detailed.

Depp sued the tabloid's publishers News Group Newspapers Ltd (NGN) and the author of a 2018 article over claims he was violent to actress and model Amber Heard, 34, during their volatile two-year marriage.

The case, which laid bare Depp's chaotic battle with drink and drugs and shattered his global reputation, was dubbed "the biggest English libel trial of the 21st century".

Judge Andrew Nicol, who presided over the libel case, dismissed the actor's appeal and ordered the paying of the defendants' costs on the basis that he was not persuaded the grounds for appeal had a "reasonable prospect of success".

Despite the rejection of this appeal, Depp's legal team could still take the case directly to the UK's Court of Appeal.

According to the court order, Depp was ordered to pay £520,000 of the defendants' bill by December and a further £108,235 by 22 January 2021.

Depp took issue with a 2018 article in the Sun, which questioned whether author JK Rowling could be "genuinely happy casting wife beater Johnny Depp" in the Harry Potter franchise's Fantastic Beasts spin-off.

While the legal odds had initially appeared to be stacked in Depp's favour, the High Court in London found, early this month, that the article had been proven to be "substantially true".

The judge said he found that 12 of 14 alleged instances of abuse of Heard by Depp had indeed occurred.

Depp vowed to appeal against the decision calling it "surreal" in a statement and adding that "his life and career will not be defined by this moment in time".

The actor also announced that he had agreed to resign from his role as Gellert Grindelwald in the Harry Potter franchise spin-off "Fantastic Beasts" at the request of Warner Bros.

"Johnny Depp will depart the Fantastic Beasts franchise. We thank Johnny for his work on the films to date," the studio said in a statement at the time.