I should mention that my friend lives 10 mins from the hospital and her waters broke half way there. The midwife didn't believe she was in labour until she came to her house and did an internal to find her waters bulging. My friend was wheeled up to the birthing suite, got out of the chair went to lean on the bed which had no brakes on, DH went to grab her and as he did DS came out!
I would think that as soon as you feel a ctx head straight for the hospital regardless of what they may say.