Thanks @NWnature and @Zaalfruit. I can't really believe how quickly it all happened. I started having period type pains in the evening and tracked them using an app, but they were all over the place and when I called the hospital they said I didn't need to come in yet. Then all of a sudden the contractions were two and a half minutes apart and so strong I couldn't even sit in the bath. By the time my husband had called the hospital and we were out the door, I could already feel myself starting to push. Five minutes later my husband was calling an ambulance while still driving and I was screaming down the phone "She's coming out now!". He just had time to pull over on a roundabout as I pulled my leggings down, crouched on the passenger seat and guided her out with my hands. The cord was round her neck and she didn't breath for a few seconds (which felt like a lifetime), but thankfully I was on the phone to someone from the ambulance service and they talked me through it. Then the ambulance people turned up and cut me out of my leggings to get us untangled. We still need to work out how to clean the blood etc. out of the car properly!
I think I'm slightly traumatised by it, but I suppose it is a good story and it showed me what my body can do without any help. Apparently it's likely to be even faster next time (if I can brave a next time!), and they've said I should have a home birth to prevent it happening again.