After forcing their way in, they found the bodies of the mother, believed to be aged 37, and two daughters, believed to be aged 13.
The 45-year-old father, who was missing from the address, was found hanging in Woodford Reservoir in Walthamstow, north east London, early this morning.
Post-mortem examinations are being carried out but police said the bodies of the female victims had no signs of visible injuries.
The father has been named locally as Pullarkattil Rethishkumar and the twin girls named as Niya and Neha Rethishkumar by friends who went to pay respects at the house where they died.
The 13-year-olds, who were in Year 8 at the Chadwell Heath Academy, were “kind” and “shy” girls and were inseparable.
Arjan Padam, 13, who was in Niya’s form, said:
The family had lived in the east London ground-floor flat for around eight years, according to one neighbour. She added:
A school friend of the twins said:
Police are also under investigation after the bodies were found at the property the day after officers were called there but left – because there was no answer.