The discovery was made after police forced their way into the home in Bedfont, near Hounslow, West London just after 3pm on Friday.
They had been called after concerns were raised about the occupants.
Last night, police named the family as Michal, 39, Monika, 35, Maja, 11, and Dawid Wlodarczyk, three.
They are not looking for anyone else in connection with the tragedy.
The family's next of kin have been informed and are being supported by family liaison officers.
Speaking at the scene, Chief Superintendent Sean Wilson, The Met's policing commander in west London, said post-mortem examinations were being arranged to determine how they died.
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