The jury returned a unanimous guilty verdict at Coutts's trial

Graham Coutts, 36, of Waterloo Street, Hove was convicted in February of murdering the Brighton school teacher.

One ground for the appeal is that the trial judge did not tell the jury a manslaughter verdict was open to them.

The court was told the crucial issue was whether it was a deliberate killing or an accident during consensual sex.

'Dangerous act'

Miss Longhurst was strangled with a pair of tights in March 2003, but Coutts claimed it was accident.

After her death he kept her body in a storage unit for weeks before setting it on fire at a beauty spot in West Sussex.

Edward Fitzgerald QC said: "The judge decided not to leave the alternative verdict of manslaughter although the Crown conceded there was a legal basis for it.

Jane Longhurst was a special needs teacher and musician in Brighton

"There clearly was a viable basis for a verdict of manslaughter both on the basis that the appellant's (Coutts) unlawful and dangerous act of tightening the ligature led to death, and on the basis of gross negligence."

Mr Fitzgerald told the appeal there was no dispute Coutts, who was jailed for a minimum of 30 years at Lewes Crown Court, was responsible for Miss Longhurst's death.

"The crucial issue was whether this was a deliberate killing to satisfy sadistic and necrophiliac tendencies, or an accident that occurred in the course of consensual sex by the mechanism of vagal inhibition," he said.

Another ground for Coutts's appeal relates to evidence at the trial about his interest in violent pornography on the internet.

Internet evidence

Mr Fitzgerald said the Crown's deliberate killing claim was in part supported by the internet evidence.

"But, the Crown had themselves recognised that, without the internet evidence, there was reason for a jury to infer that this was simply an accident in the course of asphyxial sexual intercourse," he said.

The case at London's Court of Appeal is being heard before Lord Chief Justice Woolf sitting with two other judges and is expected to last two days.

Miss Longhurst, originally from Reading, Berkshire, was a special needs teacher