The officers were on route to the scene when further calls were received reporting the Skoda had been involved in a head-on collision with a Toyota, the force said.
The 42-year-old man driving the Toyota, as well as a 33-year-old woman and two boys aged 15 and seven, all from Glasgow, were pronounced dead at the scene.
The 40-year-old Cambridgeshire man driving the Skoda was also declared dead at the crash site.
READ MORE: Two children from Glasgow among five killed in fatal collision
A third boy in the Toyota, also aged seven, was airlifted to the Royal Victoria Infirmary in Newcastle where he remains in a serious condition.
All six people involved in the crash have yet to be formally identified.
Photographs on social media showed a plume of black smoke rising into the sky above the motorway at the site of the crash.
The images also showed the tailbacks created by the incident, with traffic backed up across all three lanes of the motorway.
Four fire engines from nearby Penrith, Kendal and Shap were mobilised following the incident, and fire crews remained at the scene for several hours.
A spokesperson for Cumbria Police said: “The families of those involved are being supported by specially trained officers.
“Officers would like to thank members of the public that assisted at the scene and those affected by the collision for their patience.
“We would also like to thank those that have already been in touch who witnessed or have dashcam of the incident, we continue the appeal to anyone with information or with dashcam to contacts us.
“Anyone with information relating to this incident can report online at www.cumbria.police.uk/report-it, quoting incident number 146 of 15 October.
“You can also phone on 101. Alternatively, you can contact Crimestoppers, anonymously, on 0800 555 111.”
