THE man convicted of the brutal murder of teenager Lorna Porter yesterday succeeded where convicted Ice-Cream War killers T C Campbell and Joseph Steele failed in persuading the Court of Criminal Appeal to hear fresh evidence.

Alexander Hall, 43, maintains he is innocent and that his conviction by the majority verdict of a jury in February 1988 amounted to a miscarriage of justice.

The fresh evidence will concentrate on an attempt to undermine the crucial testimony of George McAvoy, who claimed at the trial to have seen a man answering Hall's description with a young woman on the night of the murder.

McAvoy has now given a statement to police, claiming he invented that story from gossip, but he will not be one of the witnesses to appear before the appeal court.

Hall, a former policeman and Royal Marine, was convicted of assaulting Lorna Porter in the garden of his home in Thorn Road, Bellshill, on September 9 or 10, 1984, by repeatedly cutting her throat. His appeal against conviction was refused in March 1989, but in February last year the Scottish Secretary referred the case back to the appeal court, in the light of a number of statements obtained since the trial.

Lord Cullen, the Lord Justice- Clerk, who heard the case with Lords Kirkwood and Osborne, said that about 10.43pm on Sunday, September 9, 1984, Lorna Porter, then 18, had arrived by train at Bellshill, having spent the weekend with her fiance in Drumchapel. She sometimes called at Hall's house to visit his wife, who was her fiance's sister, but on this occasion Mrs Hall was not at home.

One of the main sources of evidence against Hall was a statement he allegedly gave to police after he was stopped for road traffic offences in July 1985. He was alleged to have said: ''I've nothing to live for. I did Lorna in. I split her. It's getting to me. I'm doing myself in. I've nothing else to live for.'' Hall denied making any incriminating statement.

The Crown still needed evidence to corroborate that alleged confession, and relied on George McAvoy, who had been in Bellshill that night looking for Mrs Jean Carroll, with whom he had been living but had quarrelled. He claimed that, as he was standing outside the door of the miners' welfare club opposite Hall's house, he saw a man arguing with a young girl. He heard the man say: ''F*** him'' and grab the woman by the arm.

The Crown maintained that this linked Hall to the murder, and argued that Hall must have frog-marched Miss Porter across waste ground behind his house to the lane where her body was found.

Lord Cullen said Mr Michael McSherry, solicitor-advocate for Hall, had explained that George McAvoy's brother, James - who did not give evidence at the trial - had now sworn an affidavit to the effect that his brother could not have been at the miners' welfare club when he said he was.

James McAvoy, too, had been in a sexual relationship with Mrs Carroll and waited for her outside her daughter's house in Bellshill that night. He saw his brother approach just after 10pm and patrol round the flats until after midnight.

The appeal court will also hear the evidence of Mrs Carroll, who had now also given a statement that she had seen George McAvoy outside her daughter's house that night.