The police described the double murder as one of the 'most horrific' they had ever come across.
The bodies were found by Ms Bisset's boyfriend, who has been eliminated from the investigation, on Thursday morning at her basement flat in Heathfield Terrace, Plumstead, south-east London.
Two witnesses heard a man and woman arguing 'in the vicinity' of the flat between 10pm and 11pm on Wednesday.
Det Supt Mike Banks, who is on the inquiry team, said: 'We believe the argument was from inside the flat where she was killed. I think it could have been her killer arguing. We hope people who may have heard them will contact us.'
Yesterday the boyfriend of Ms Bisset, 27, also disclosed that the family had been frightened last week by a stranger who was seen staring through a window at their home.
Ms Bisset's body was severely mutilated and her daughter, Jazmine, was found suffocated in her bed.
The mother was last seen when she picked up her daughter from a nursery school on Wednesday afternoon. They were driven home in a minicab, whose driver has been questioned by the police.
Jazmine's father, who lives in south-west England, contacted the police and will be questioned today.
Police have revealed that Ms Bisset was extremely security-conscious, and believe it is very unlikely that she would have let a stranger into her home. There was no sign of a break-in or a sexual attack, and nothing had been taken.
Blood was found in the kitchen sink, where police believe the killer tried to clean himself. The murder weapon, which is believed to be a knife at least six inches long, has not been recovered. The attacker, or attackers, would have been covered in blood, according to the police.
Ms Bisset's boyfriend said yesterday that she had been upset about a week ago when she saw a man looking through the back window of the flat.
She was described as a 'totally devoted mother'. The walls of the flat were covered with pictures Jazmine had painted. Ms Bisset was described as 'quiet and artistic'.
Det Chief Supt Bill Ilsley, who is heading the inquiry, said: 'The person who did this is a danger to society and must be caught. I don't know how they can live with themselves.
'The injuries were horrific. They could not be worse. It was a frenzied attack and that's why it's vitally important that we identify the killer or killers as soon as possible.'
Police are appealing for further information. They described the response so far as 'magnificent'. The murder inquiry telephone number is 081- 312 1200.Reuse content