Cumbria Constabulary said officers first received a report of a Skoda travelling southbound on the northbound carriageway.
Emergency crews were en route when the force received further calls it had been involved in a head-on collision with a Toyota.
Jaroslaw Rossa, 42, the driver of the Toyota, and his two sons, Filip, 15, and Dominic, seven, were pronounced dead at the scene alongside passenger Jade McEnroe, 33.
Richard Woods, the 40-year-old Skoda driver from Cambridgeshire, also died in the crash.
Lochend Community High School and Oakwood Primary School in Glasgow have paid tribute to both Filip and Dominic.
Lochend headteacher Katy Anderson said the school community was in “shock” over the death of Filip.
She added: “He was a well-loved and respected young person who has touched the lives of so many in our school community and was our school chess champion.
“A highly intelligent, caring boy with a brilliant sense of humour, Filip was particularly fond of his science subjects and aspired to go to university to study either architecture or science.
“Filip was always the first to help in a situation and it is now our turn to help and send our love to his family and friends at this heartbreaking time.
“We will do everything that we can to support the family and navigate our school community through this devastating situation.”
