I have copied the following from here (my highlights)
http://www.adviceguide.org.uk/index/your_world/travel/traffic_accidents.htm#traf...Payment for hospital treatment
Immediate treatment
The driver of a vehicle involved in a road accident may be charged for any emergency medical treatment provided by a doctor (other than one working in or called from a hospital), for example, a doctor who is off duty and happens to be passing by the accident. There is a standard charge plus, in certain circumstances, a mileage allowance. The driver will receive a bill from the doctor some time after the accident. This charge should be included as part of any claim for damages.
The driver’s insurance company will usually pay this charge without affecting their no-claims bonus.
Further hospital treatment
In England, Wales and Scotland, if anyone involved in the accident receives further hospital treatment in a non-NHS hospital, as an in-patient or an out-patient, the hospital may claim from the driver’s insurance company up to £2949 for the cost of treatment as an inpatient and up to £295 for the cost of treatment as an outpatient. In Northern Ireland, this applies only to in-patients in both NHS and non-NHS hospitals. The hospital will write to the patient, or their parents if a child was injured, asking for the driver’s name and address, details of their insurance company, whether or not the patient is making a claim against the driver and if a solicitor is acting for the patient.
If someone has a road accident and receives further hospital treatment at an NHS hospital, the Department of Health (in Scotland, the Health Department) can require the insurance company of the other driver to meet some of the costs.
Where the driver who caused the accident is not insured or cannot be traced, the costs will be recovered from the Motor Insurers’ Bureau (MIB).The Department of Health automatically recovers NHS charges from the insurance company on behalf of the hospital. There is no need for the person to be involved in routine cases. In cases where the person takes civil legal action against the other party, there is no need to include a claim for NHS charge recovery.If you have problems about being asked to pay for medical treatment after a road accident, you should consult an experienced adviser for example, at a Citizens Advice Bureau.