If I am not mistaken, emergency services won't/can't claim for their services (in obvious circumstances of negligence) because their is a concern that people needing assistance may hold off on calling due to the costs involved. However, this may have changed and may only apply to certain services? :
Many moons ago, when I was young and reckless, I 'borrowed' a car. I was an inexperienced driver so ended up smashing it up and spent a week in intensive care/hospital. When I was eventually released I was billed for the ambulance trip from the crash site to the hospital. I don't think I got a charge from the Fire Brigade who cut me out but not sure.