Following a three-week trial in July last year, Mr Justice Nicol dismissed the Hollywood star’s libel claim against the publisher of The Sun finding that an April 2018 column calling Mr Depp a “wife beater” was “substantially true”.
The actor is now asking the Court of Appeal to grant permission for him to challenge the ruling, with the aim of having its findings overturned and a retrial ordered.
Mr Depp is trying to overturn last year’s ruling on the basis Ms Heard lied about giving the entirety of her seven million US dollar (£5.5 million) payout to charity.
Lawyers for the actor allege that the Aquaman actress has been basking in the glow of philanthropy when in fact only a fraction of the millions she promised to two charities has ever reached them.
Mr Justice Nicol said at the time he rejected allegations Ms Heard was out to profit from her ex financially, saying: “Her donation of the seven million US dollars to charity is hardly the act one would expect of a gold-digger.”
The actor’s legal team say his ex-wife had effectively “tipped the scales” against him through exaggerated claims of her own generosity.
At a hearing at the High Court on Thursday, lawyers for Mr Depp submitted evidence allegedly proving that only a fraction of the settlement has been paid to the two charities it was promised to.
They alleged just 100,000 dollars (£72,000) was paid to the Children’s Hospital of Los Angeles – paid directly by her ex-husband’s accountants – and only 450,000 dollars (£322,000) had reached the American Civil Liberties Union (ACLU).
In a statement made in August 2016, Ms Heard vowed that 3.5 million dollars (£2.5 million) would be given to each charity.
Mr Depp’s lawyers say the fact Ms Heard has appeared to assert publicly that all the money she received from her ex-husband has already been given away undermines her credibility as a witness.
Andrew Caldecott QC, for Mr Depp, said that the claims had given Ms Heard “a considerable boost to her credibility as a person”.
He added that it had “tipped the scales against Mr Depp from the very beginning”.
In a statement submitted to the libel trial, Ms Heard seemed to confirm that the money had already been paid.
It read: “I remained financially independent from (Mr Depp) the whole time we were together and the entire amount of my divorce settlement was donated to charity.
“In fact, my desire to remain financially independent was one of the main sources of conflict during our relationship.”
The actor’s lawyers said the fact the full sum had not been paid came to light following a subpoena in Mr Depp’s defamation lawsuit against Ms Heard in the US, adding that she strongly resisted disclosing the information.
Joelle Rich, one of Mr Depp’s solicitors, said Ms Heard had not been challenged on this during the trial because “it had been accepted at face value”.
In a statement submitted to the court, she said: “If Ms Heard wilfully gave false evidence about giving a substantial amount of money to a children’s hospital and an organisation which campaigns on behalf of victims of domestic violence, then it will be submitted on the appellant’s behalf that she was clearly capable of lying about her relationship with Mr Depp.”
Adam Wolanski QC, representing The Sun’s publisher News Group Newspapers (NGN), said the evidence would not have impacted the trial outcome.
He said Mr Depp’s attempts to characterise Ms Heard as a gold-digger was “a misogynistic trope”.
He said the new evidence did also not prove that Ms Heard had lied.
Mr Wolanski said Ms Heard had said she “donated the money, not that she had paid it”.
He added: “A donation is not the same as a payment and we know that not least because this is how the charities themselves have understood what Ms Heard has done”.
He said the American Civil Liberties Union (ACLU) “understood” that Ms Heard had “pledged to pay over 10 years – that is a donation”.
He added that she “has made a number of payments already in pursuance of these pledges”, telling the court that she had paid “in total, some 950,000 dollars (£681,152) to the ACLU and 850,000 dollars (£609,452) to the Children’s Hospital Los Angeles”.
Lord Justice Underhill said the court would give judgment at a later date.