The victims have been formally identified today as PC Dave Fields, aged 45, and Lorraine Stephenson, aged 61, who both died in a collision between two vehicles on the the A57 near Shirebrook Valley Nature Reserve at around 8.15pm.
PC Fields’ family have released a photograph and paid tribute to him in a statement, which read: "Dave was a loving husband and dad of two, who was a dedicated officer committed to his job.
"We are heartbroken by our loss and ask that our privacy please be respected at this devastating time.”
Ms Stephenson was a passenger in a silver Citroen C3, which was involved in a crash with the marked BMW3 series police car driven by PC Fields, who was responding to an incident.
Both were pronounced dead shortly after the collision.
Hundreds of people paid tribute online to the pair.
It has also emerged that PC Fields was also a well-known football referee and was vice-chairman of Sheffield Referees Association.
A statement on the association's Facebook page said: "Dave wasn't just my best friend, he was vice chairman of Sheffield Referees Association, the greatest mentor to referees, and especially to my kids. He was a referee, tutor and one of the good guys. Giving up his time to help anyone.
"Most of all he was a dad and husband and my thoughts are so so much with his family at such a difficult time. He loves football and loves his job as a police officer and his passing will leave a hole in so many lives."
Commenting on the association's post, Andy Hogg wrote: "Dave Fields - lover of football, lover of refereeing, lover of people, lover of life. "He was not in the Premier League of top blokes, he was in the Champions League."
Clinton Cooper wrote: "My involvement with Sheffield Referees Association allowed me to meet and work with some wonderful people over many years. None finer than Dave.
Trevor Sherwood, editor of Crime and Policing News Website, said: "This is a very tragic incident that has happened on Christmas Day.
"We have lost a member of the thin blue line and tragically a member of the public also."
Specialist officers are currently working to support both families at this difficult time.
The driver of the Citroen, a 63-year-old man, was taken to hospital where he currently remains in a serious condition.
The Independent Police Complaints Commission is investigating.
A South Yorkshire Police spokesperson said: "Witnesses to the collision, or who saw either of the vehicles prior to the incident, are asked to call 101 quoting incident number 691 of 25 December 2017.
"We are aware of a fundraising page set up to collect donations for the families of those affected by this incident. Officers want to remind the public to be careful to verify any websites of this nature and only donate to legitimate pages."