The two women, aged 22 and 49, were found suffering from serious stab wounds in Northdown Road just after 12.30am on Monday.
Despite being treated by emergency services, both were confirmed dead at the scene.
Officers are now making urgent attempts to arrest a male suspect, who they say is known to the victims.
Detective Inspector Caroline Corfield, from the force’s homicide team, said: “What has happened this morning is truly devastating and heart-breaking. Our thoughts go out to the two victim’s family and friends at this traumatic time.
“Tragically there was nothing which could be done to save them and we are working to establish the circumstances behind what happened.”
Appeals are being made for the man to hand himself in.
Anyone with information has been asked to contact 999.