There is a busy dual carriageway near me with almost no cyclists but I often see ambulances struggling to make their way through the queues. Presumably paramedics will also be calling for cars to be banned from busy roads at peak times - they should be able to get through without any problems with all the cars out the way.
As an aside, working in a hospital A&E staff seem to have a real downer on cyclists, if a cyclist (or motorcyclist) comes in injured it must be their fault or they were drunk but if a car driver comes in it must be some tragic accident.