Ms Bisset was stabbed more than 70 times and dismembered with what is believed to have been a knife with a 7in blade. Her daughter Jazmine was suffocated. The bodies were found by Ms Bisset's boyfriend on Thursday at her flat in Plumstead, south-east London.
Police, who are building up a picture of events preceding the killings, say the frenzied nature of the attack indicated that the killer had been under the influence of the drug crack.
Officers said that witnesses had described a man wearing a cream top being spotted near the victims' home on two occasions in the days leading up to the killings.
Detective Superintendent Michael Banks, of the Metropolitan Police, said yesterday: 'Samantha specifically told her boyfriend she had seen from the veranda somebody looking into her flat from the rear of the premises a week before she died.
'Obviously we want to trace that man and speak to him. He may have had nothing to do with the murders but the green he was standing on at the back of the flat leads nowhere.'
It was disclosed yesterday that a witness saw a man in a cream coloured jacket with a dark collar knocking at the door of the flat at about 10.30pm on Wednesday.
A couple have described seeing a man in a cream top watching the flat on Saturday, 30 October, as they walked their dog.
Susan Dewar, 37, a hairdresser whose home overlooks the house where Ms Bisset was killed, also reported seeing a 'strange man' staring at her from behind a garden wall a few days before the killings.
Her husband, Terry, 36, said Ms Bisset, who he described as having a 'hippy image', would frequently sunbathe in her garden which was overlooked by nearby flats.
Det Supt Banks said: 'What possible motive could anyone have for coldly and callously killing a four- year-old child, unless she knew the attacker or possibly witnessed the attack on her mother?
'Samantha was one of those people who was very, very careful about who she let in. In fact a couple of weeks ago a gas board official had a hell of a time getting in.
'But she did have a habit of leaving the veranda door open and when we got there we found it was open slightly.'
He added: 'It's possible the killer disturbed them as they slept. Samantha was in her dressing-gown when she was killed and Jazmine was also dressed for bed, but it could have been they were up watching television rather than in bed.'
A taxi-driver was apparently the last to see them alive, at about 3.40pm on Wednesday.
Neighbours reported hearing a row between a man and a woman at the flat between 10.30pm and 11pm on Wednesday.
Police believe that the attacker's clothes will have been heavily bloodstained. There were signs that some blood had been washed off in the kitchen sink. The murder weapon has not yet been recovered.
Detectives have questioned Ms Bisset's boyfriend and eliminated him from their inquiries. They have also contacted Jazmine's father, described as 'a hippy-type traveller'.Reuse content