A 30-year-old woman and a 23-year-old man died alongside the four-year-old girl after a blaze at a former station house in the village of Rushton, near Kettering, on Friday night, Northamptonshire Police said.
A man from Kettering was arrested on suspicion of murder on Saturday and remains in police custody, the force added.
The victims’ next of kin have been informed and are being supported by specially trained officers.
In a statement on Sunday afternoon, chief inspector Paul Cash said: “We know this incident has caused significant distress locally and our officers will remain in the area to provide reassurance and help where we can.
“In relation to this investigation, one arrest has been made, and we will provide updates surrounding this as soon as we can.
“This investigation is well under way but remains in its early stages, and it will take time to fully establish what has happened.”
Specialist fire investigators and investigation dogs have been deployed to support the investigation into the cause of the blaze, police said.
Senior investigating officer Detective Chief Inspector Ruby Burrow, of the East Midlands Special Operations Unit, said: “This is a heartbreaking situation and my thoughts, and those of everyone involved in responding to this fire, are with the people who died and those who love them.
“An incredibly thorough and complex investigation is underway with our partners in Northamptonshire Fire and Rescue Service to make sure we get the answers that loved ones need and deserve.
“Due to the intensity of the fire we are managing a very challenging and dangerous scene, and are working with partners to safely and respectfully recover the deceased to enable formal identification to take place.”
After the fire, one person was taken to hospital by the East Midlands Ambulance Service and three officers were assessed because of smoke inhalation, Northamptonshire Police said.
Photographs show a large hole burned through the roof of the building – a 19th-century former station master’s house at the now-closed Glendon and Rushton railway station.
It is a Grade II-listed building, according to the Historic England website, and is now believed to be a residential property.
Train services between London St Pancras International and Corby, Derby, Nottingham and Sheffield were disrupted on Saturday after the fire.
The disruption was due to damage caused to a railway line, according to the National Rail website.
