The killings were called “wicked” acts by one judge, Judge Goose, as he ordered Allen to serve at least 37 years in prison when he was sentenced in June 2021.

Allen was cleared of Ms Class’s murder in 2000, but that acquittal was overturned in 2019 after “compelling” new evidence was personally presented to the Court of Appeal judges by Director of Public Prosecutions Max Hill QC.

Allen denied killing either of the women, but was found guilty of two counts of murder by a jury that heard eight weeks of evidence.

On Thursday, he lodged a new appeal against his murder convictions and sentence at the Royal Courts of Justice in London.

Lord Justice Holroyde, sitting with Madam Justice McGowan and Mr Justice Choudhury, dismissed his appeal after an hour-long hearing.

Katherine Goddard QC, representing Allen, focused her arguments on the trial judge’s summary of evidence relating to Ms Grlakova before the jury considered their verdict.

She claimed the judge had “misdirected” the jurors in such a way that it had the effect of encouraging them to dismiss the testimony of three defense witnesses as “unreliable and uncredible”.

Ms Goddard said the three witnesses, who did not know Allen, claimed to have seen Ms Grlakova after Boxing Day 2018, which could ‘fundamentally undermine a key part of the prosecution’s case’ that she was killed late in the day or early the next day.

“If any of these observations were or could be correct, we submit that they cast doubt on the whole premise of the crown case,” she said.

The court was then told that jurors had been allowed to consider evidence relating to Ms Class’s murder, with Ms Goddard arguing that the judge’s alleged errors could also make the conviction for her death dangerous.

Challenging Allen’s sentence, she also argued that there was no evidence that either murder was planned or premeditated.

Alistair MacDonald QC, representing the Crown Prosecution Service, said Allen’s argument against his conviction was ‘ill-conceived’ and pointed to a ‘wealth’ of ‘compelling evidence’ which supported Allen ‘was the killer of Ms Grlakova”.

This included Allen being one of the last people to see her alive, cellphone evidence that he had visited the site where she was found and evidence that he had bought a trowel and gloves from a supermarket. that would have been used for the disposal of his body, the court heard.

Mr MacDonald added of the witnesses: ‘The judge fairly advised the jury on how to deal with this evidence.’

He said Ms Grlakova had ‘effectively disappeared off the face of the earth’ on Boxing Day 2018, despite police then poring through 6,000 hours of CCTV.

Allen, dressed in a blue shirt and seated at a table, followed the hearing via video link from HMP Wakefield in West Yorkshire.

Ms Grlakova’s widower, who had been estranged from his wife, was also listening to the proceedings remotely, the court heard.

Dismissing the appeal, Lord Justice Holroyde said of the trial judge: “All he did, and in our view rightly did, was to give a fair summary of the evidence of the witnesses and briefly mention the need to be careful with identification evidence.

“The finding was neither inappropriate nor unfair,” he added.

He also concluded that the sentence given to Allen was not “grossly excessive”, noting that the judge considered aggravating factors in the case.

At Allen’s trial, jurors heard harrowing details of how the body of Ms Class, 29, who worked in the sex industry, was found by children on the banks of the Humber in October 1997 .

She had 33 different injuries.

Ms Class left behind three children, Sophia, Aiden and Lewis.

Ms Grlakova’s body was found naked in a stream in Rotherham in April 2019, four months after she was last seen on Boxing Day 2018.

The 38-year-old man had been strangled.

She was from Slovakia and moved to the UK in 2008 but, after being away from her husband and children, she started working in the sex industry.

Sheffield Crown Court heard how Allen attacked two sex workers in 2000 in Plymouth, just weeks after he was acquitted of Ms Class’s murder.

After being imprisoned for these attacks, he told a probation officer of his dislike of sex workers and women in general, saying, “I like to scare them. I like to cause pain.

“I like to make them cry. I like blood. I like hurting them. I appreciate. It makes me feel good.”

In 2010, Humberside Police launched an elaborate sting operation to assess the danger posed by Allen.

He told one of the undercover officers how a sex worker got mad at him ‘so I strangled her and threw her in the Humber’.

The jury was told this was the ‘clearest possible admission’ of Ms Class’s murder.

Following Allen’s convictions, police forces across the UK were told to check unsolved cases to ensure that Allen had not committed any other offences.