Former Metropolitan Police officers Jonathon Cobban and Joel Borders were each handed a three-month jail sentence for sending the messages on a public communications network.

They sent the messages in a WhatsApp group chat said to be called "Bottle and Stoppers" - which included convicted rapist and killer Couzens, who murdered 33-year-old marketing executive Sarah Everard in March 2020.

They joked about raping a female colleague, talked about tasering children and people with disabilities, and displayed racist views in the group chat, Westminster Magistrates' Court heard in November 2022.

The court was told that in one exchange, Borders wrote: "I can't wait to get on guns so I can shoot some c*** in the face!"

In another, Cobban joked about sexually abusing domestic violence survivors whom he said "love it... that's why they are repeat victims more often than not".

During a hearing last month, lawyers representing both men brought an appeal against their convictions and sentences at the High Court in London.

But in a ruling on Friday, the Lady Chief Justice Baroness Carr and Mr Justice Saini dismissed the appeal.

In a summary of their decision, Baroness Carr said the pair "could have no reasonable expectation of privacy" over the messages which "relate to policing actions".

"The stand-out feature of the offending was the enormous indirect 'societal' harm caused by the loss to public confidence in the police," she added.

Following the ruling, the most senior judge in England and Wales said the two men would have 28 days to "reflect maturely" on whether to make a Supreme Court bid.

If the pair - who were granted bail after their sentencing - decide not to make a bid for a challenge at the UK's highest court, they will need to return to Westminster Magistrates' Court within 10 days.

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At a court hearing on 26 June, Nicholas Yeo, representing the two men, argued to judges that the offence they were convicted of "does not extend to private consensual messaging".

Instead, he claimed, it is aimed at messages "that would not be welcomed by the addressee".

He said: "If one looks at the word indecent, it would be absurd to conclude that it applies to wanted indecent messages."

Mr Yeo continued in written submissions: "It is lawful to send jokey, bombastic and iconoclastic messages to a closed group of people who will not be grossly offended thereby."

But Jocelyn Ledward KC, for the Director of Public Prosecutions, said there had been no mistakes in the previous judge's decision and that the argument over the law was "fundamentally misconceived".

She said in written submissions: "The provision is not exclusively concerned with protecting people from receipt of unsolicited messages of the proscribed character, but is rather aimed at ensuring propriety in communications over electronic public networks."