Sabrina Kouider, 36, and her partner Ouissem Medouni, 41, killed 21-year-old Sophie Lionnet over an entirely false belief she was having an affair and colluding with ex-Boyzone singer Mark Walton, at their home in Wimbledon, south-west London.
The pair were jailed for life and ordered to serve at least 30 years behind bars at the Old Bailey in June 2018 after being found guilty of murder.
The dead body of Sophie was discovered on September 20 2017 after neighbours complained about the smoke.
When asked by firefighters, Medouni claimed the au pair’s body was the remains of a sheep bought from a local market.
The couple were found guilty of murder, having admitted perverting the course of justice in relation to the disposal of Ms Lionnet’s body.
They each challenged their minimum terms at a hearing in London, while Medouni also launched a bid to appeal against his conviction, but their cases were dismissed by senior judges.
But their appeal bids were rejected by Lady Justice Hallett, sitting with Mrs Justice McGowan and Sir John Royce.
The judge said reasons for the court’s decision will be given at a later date.