POLICE have had a "positive response" to their latest appeal in their investigation into a deliberate house fire which left a man dead and a woman injured.

Cameron Logan, 23, was killed in the fire at his family home on Achray Place, Milngavie, East Dunbartonshire, in the early hours of New Year's Day.

His girlfriend Rebecca Williams, 24, known as Bex, is in a serious condition in hospital after being injured in the blaze.

Police have issued various witness appeals and said a number of people have come forward with information, including individuals who believe they may be the dog walkers sought in earlier appeals.

But officers said they still want to speak to anyone else who may have information. In particular they are seeking a man in army combat clothing reported to have been walking on the West Highland Way on the morning of the fire.

It is believed he routinely walks from Maryhill to the West Highland Way at Craigton Road, often passing through the Milngavie area, and officers believe he may have information which could help the ongoing probe.

On Friday, police said a number of people had come forward with information, but they were still keen to speak to others.

Officers, who were called to the fire at 7.25am on January 1, are treating the case as one of murder and attempted murder. The fire also resulted in Logan's parents being treated for smoke inhalation and caused the death of the family dog.

Williams, a broadcast journalist with Global Radio, was taken to the Queen Elizabeth University Hospital in Glasgow, in a critical condition. Her condition remains serious but stable, according to the hospital.

Williams' father, Phillip, has said she is "fighting hard" in hospital.

Williams and Logan had been celebrating Hogmanay and walked home in the early hours of the morning.

Detectives say the fire had been set deliberately, resulting in the death of psychology student Logan.

Since then, officers have also been carrying out door-to-door inquires, checking CCTV footage and interviewing people from the party the couple attended.

Officers were seen searching woodland and waterways near the semi-detached property on Friday.

Detective Chief Inspector Paul Livingstone, of the Major Investigation Teams at Govan, thanked those who have already come forward with information.

He said: "We continue to seek information on the dark-coloured car that reportedly had its engine running at the lay-by on Craigton Road and we would continue to ask anyone with information to come forward."