The woman gave birth shortly afterwards.
But when Parker lifted the baby onto the mum, he realised the umbilical cord was wrapped around the newborn's neck.
"It all happened so quickly," Parker said.
He untangled the cord and made sure the baby was breathing. An ambulance arrived shortly after.
Mum and baby were doing well, police said this morning, despite the dramatic birth on the side of a road.
A humble Parker said he only assisted.
"It was all the mother, I just ended up being in the right place at the right time," he said.
"The mother did extremely well, especially under the circumstances."
Parker - who has two children of his own - said he hadn't been expecting to attend another birth any time soon.
"In 10 years on the job I haven't been in a situation like this before."
But after the drama and excitement of the birth, it was back to porridge for Parker, who continued his usual duties after the ambulance arrived and staff took over.
"This is what makes the job so exciting and rewarding, when you're part of something like this."