Hollywood star Johnny Depp has been refused the right to appeal a verdict that upheld claims in a newspaper article he beat his ex-wife and fellow actor Amber Heard, a UK court has ruled.

Two judges at the Court of Appeal dismissed his application to challenge a lower court ruling in his high-profile libel claim against The Sun for a 2018 article that called him a "wife-beater."

It said the hearing in the High Court had been "full and fair" and the judge "gave thorough reasons for his conclusions, which have not been shown even arguably to be vitiated by any error of approach or mistake of law."

The judge in the November decision ruled against the Pirates of the Caribbean actor in his libel claim and ordered him to pay the newspaper's publisher, News Group Newspapers (NGN), 628,000 pounds ($873,000) in legal costs.

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In his application for the appeal earlier this month, Depp's lawyers cast doubt on testimony given by Heard at the original libel trial.

They argued that submissions made, saying she had given the whole of her divorce settlement to charity, had prejudiced the case against Depp, while arguing only a fraction of the settlement had been handed over.

The Court of Appeal judgment said Depp was unlikely to "overturn the findings of a trial judge on purely factual questions."

A spokeswoman for The Sun said after the ruling that the newspaper "had every confidence that this leave to appeal application would not be granted and are pleased with today's decision."

She added: "The case had a full, fair and proper hearing and today's decision vindicates the courageous evidence that Amber Heard gave to the court about domestic abuse, despite repeated attempts to undermine and silence her by the perpetrator."

The failed libel action has already damaged Depp's career, with the actor saying afterwards he was asked to step down from his role in the Fantastic Beasts film franchise based on the books by Harry Potter author JK Rowling.

The case, which laid bare the actor's battle with drink and drugs, was called "the biggest English libel trial of the 21st century."

NGN relied on the defense of truth, arguing it had a valid basis for the 2018 story by detailing 14 alleged instances of Depp abusing Heard.

The judge in the original case dismissed Depp's claim after three weeks of revelations about the couple's stormy relationship, saying the article had been proved to be "substantially true."