Lucy Kelly's waters broke while the 25-year-old was being driven to hospital in Exeter by her partner Chris Haggar on 27 December.
Mr Haggar managed to get the attention of two passing police vehicles.
Within five minutes of the female officers arriving, baby Lily was delivered at the roadside.
The couple were driving from their home in Cranbrook to the Royal Devon and Exeter Hospital, a journey of about 20 minutes.
Ms Kelly said: "We were only two or three minutes away from the hospital but it all just happened so quickly".
"We had been in the car for five or ten minutes when my waters went and Chris said I should call the ambulance rather than the midwife because we needed help now.
"So I got them on speaker phone and we were both shouting - it was tense."
She said the paramedic call handlers told them to pull over, by which time the baby was being born.
Mr Haggar then managed to flag down the police vehicles, and the two officers came over to help.
Ms Kelly said "within five minutes of the police arriving it was all over. They were amazing".
She said the experience was very different to the birth of her first daughter, which happened in hospital.
"Olivia's birth was really controlled and I was really relaxed because I knew I was in the best place.
"But this time it all happened in less than an hour, on two paracetamol and in a car."
When the ambulance arrived, Ms Kelly "shuffled onto a stretcher" and they were taken to hospital - where Mr Haggar cut the umbilical cord and baby Lily was given a clean bill of health.
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Ms Kelly added "We liked the name Grace anyway, but then one of the ambulance staff was called Grace so it seemed to fit quite well as a middle name.
"We are just lucky there were no complications and it was quick."