Zoe Powell, aged 29, died in a collision in Oxford on Monday, October 12.
Her family's silver Subaru was involved in a collision with a lorry and Zoe and three of her four children – Phoebe Powell, eight, Simeon, six and Amelia, four – died at the scene.
Zoe’s husband Josh, 30, and their youngster child – an 18-month-old girl – were seriously injured but are expected to recover physically.
Senior investigating officer Sergeant Dominic Mahon said: “I would like to thank all those who have contacted police to provide witness statements and helped us with this investigation.
“Thank you also to those that stopped at the scene to offer help at what was a very distressing incident.
“I would like to pay tribute again to all of our officers and staff who have been dealing with this incident, and also extend this to our colleagues in South Central Ambulance Service, Oxfordshire Fire & Rescue Service, the John Radcliffe Hospital and Highways England.
"I also thank the Thames Valley Air Ambulance critical care team who attended the incident too, along with Dr Wassim Shamsuddin from Milton Keynes University Hospital who answered a call for an emergency doctor to attend the scene.
“I would also like to extend this thanks, on behalf of the Powell family, to all those who have sent their kind sentiments to the force via our official channels.
“This investigation is ongoing, and I would again urge people to not speculate as to the cause of this tragic collision.
“We are continuing to support the family of all of the victims, and will continue to do so while they come to terms with the enormity of what has happened.
“We are also supporting the driver of the HGV, who has co-operated fully with our investigation and provided a witness statement to police.”
Zoe and Josh were university students in Sheffield and had their first child in the city.
They moved to the village of Chinnor in Oxfordshire in 2014.