I've been in an ambulance once in my life when I was knocked off my motorcycle. at the time we didn't know what injuries I had, I was strapped to a back board with my head and neck braced against any movement. What annoyed me the most was I didn't even get blues and twos back to the hospital!
he even sodding stopped at traffic lights all the way there.
As others say, I'd make my own way there unless I physically can't. I recall having a badly burned thumb from one day working at the restaurant. I was just putting a flaming sambuca down when the guy deceided to jump up without looking, it went all over my hand and I couldn't get past him to the sink to put it out before the liqued burned away[1]. I ended up driving to hospital with a pint glass of Ice between my legs and shoving my hand in it when the pain got too much which was most of the way there!
[1] Sambuca will burn on your skin without hurting as its the vapour that burns, you just need to make sure its out before all the liqued has gone!