Senior midwives at the Southern General Hospital, Glasgow, later apologised to mother-of-three Eva Bochnaik for care failures.
Polish-born Eva says by the time she was admitted to hospital she was in agonising pain and her baby was five minutes from being born.
Doctors had to cut her clothes to deliver son Aarin. Eva was so weak with pain she struggled to push her baby out and he stopped breathing at one point.
The 38-year-old went into labour at about noon and called the hospital at 3pm when her contractions were five minutes apart, telling midwives it was her third child.
First time mothers-to-be are generally advised to come to hospital at this time, if not sooner.
But those having their third child can be admitted when contractions are 8-10 minutes apart as labour can be faster.
However, the midwife told Eva to take a couple of paracetamol and call back in two hours.
Eva, who is from Shawlands and who has lived in Glasgow for nine years, said: "About an hour later the pain was getting so much worse and my waters broke. I noticed my baby was going to come very quickly.
"I phoned the hospital again and finally they allowed us to come into the delivery room.
"I felt as if I was going to have the baby in the taxi. When we arrived at the hospital I could not deal with the pain any more.
"The doctors had to cut my clothes so they could deliver the baby because I was exactly five minutes from having my child.
"I was given gas and air, but it didn't help much as I was in so much pain."
Eva made a formal complaint to the hospital after the birth of her son, which was in January 2011, and received a letter from Dr Jane Richmond, Consultant Obstetrician, with a written apology.
Eva says she has been left with permanent nerve damage and pain because doctors had to cut her to deliver the baby quickly as he stopped breathing.
She said: " I believe if the nurse on the phone had acknowledged it was my third child and knew labour would be very fast, this would not have happened."
A NHS Greater Glasgow And Clyde spokeswoman said: "We have written to the patient to apologise. We made the patient aware that if she remained dissatisfied she could refer her complaint to the Ombudsman
"We are satisfied the correct action was taken for this patient on admittance to maternity for the safety of her and her baby.
"But we accept the midwife who took the call from the patient had not appreciated how far along the patient's labour was at that time. "We have followed this up with the staff member involved."