Under current UK legislation, you must pay fees to the first medical practitioner to treat you following an accident. This is part of the Road Traffic Act. Some people refer to this as a charge for an ambulance. In reality this is not the case but in real life terms it is normally the ambulance men who provide the care and the account is sent to to you from the National Health Service Trust that sent the ambulance and its crew.
You are liable for this payment no matter who is blamed for causing the accident. Your insurance company will always pay the bill under this section. Just send the paperwork into them and they will remit it directly to the hospital. Or pay it yourself and get your insurance company to repay you.
Occasionally in a hectic claims environment, the claims staff can overlook the invoice if it was sent in amongst other paperwork. It's possible that you might receive a reminder from the hospital that the invoice is still outstanding. Tell the N H S Trust who your insurers are and telephone the claims office. Be forceful but please don't be angry.
Payment of this account in itself does not affect your no claims bonus. It is not treated as a claim. So, in the unlikely event that your insurers were to pay this and nothing else your bonus would remain unharmed. In reality, in an accident where someone is injured, it is unlikely there is no other types of claim to be dealt with.
Technically, if someone else is to blame for the accident you can send the invoice on to their insurance company but you are just inviting unnecessary complications. My advice is, don't bother. It makes no difference to you whichever way.
As a result of recent changes in the law, hospitals now also charge insurers for treatment given to third party victims of accidents, with certain limitations applied. These are claimed by the NHS Trust in cases where you were to blame for the accident and another person has needed treatment for the injury that you caused. This change to the regulations has dramatically increased the cost of settling claims and has thus increased your insurance premiums. Some of those inside the insurance industry consider this to be a further case of increasing taxation by stealth by the Government.