In first pregnancies labour lasts for around 12- 14 hours, the contractions will gradually build in intensity and length, most women find they are happy to stay at home in the early part of the 1st stage and know when they want to be in hospital if that is where they are having their baby. It is unusual with first babies that the labour is so quick or you have no sign of contractions that you leave it too late to get to hospital. Of course sometimes it does depend on where you live, distance to hospital, traffic delays or otherwise that may increase your journey time.
Generally speaking though if you are having an uncontrollable urge to push then that’s the point where it may be too late to go to hospital, if you did find yourself in this unfortunate circumstance, contact the maternity unit they will arrange for paramedics to attend and in some areas they will also ask the on call midwife to attend too. You can also contact the emergency ambulance services yourself.