The force said the deaths of Kanticha Sukpengpanao, 36, Jasmin Kuczynska, 12 and Natasha Kuczynska, eight, are being treated as murder after they were discovered with stab wounds to their necks on Friday.
The death of Bartlomiej Kuczynski, 45, who was also found with a stab wound to his neck, is not being treated as suspicious, and officers are not looking for anyone else in connection with the killings.
The four bodies were discovered by police at a house in Allan Bedford Crescent after a call from a member of the public on Friday morning.
Detective Chief Inspector Chris Burgess, who is leading the investigation, said: “We understand how incredibly shocking this incident is for all involved and for the wider community, and that this latest update adds to the sense of heartbreak.
“Our thoughts are with the family of those found at the property grieving such a traumatic loss.
“We would like to thank the community for their help and will continue to provide reassurance patrols in the area.
“A cordon will remain on at the address whilst we finalise our detailed examination of the scene.”
The incident has been referred to the Independent Office of Police Conduct due to a 999 call made from a man at the address earlier on Friday morning, which did not result in the deployment of officers, and over police contact at the address on December 14, relating to a missing person inquiry.