My wife works for the NHS in the community and pays for a company car so she can have use of it out of work .
One day while traveling to a patient she was run off the road and suffered injury to her wrist and knee . She was told she couldn't make a claim for her injury because the car is only insured 3rd party and because the 3rd party can't be found there's no one for the insurance to claim .
I can't be leave that the NHS can set up insurance on a car were any injury to the staff member driving could end up being injured and not covered .
We all have that same cover if we have NHS leased cars. Who told her that? My colleague who has a lease car only has to pay the excess when she's had accidents, so her cover must be comprehensive. However, the lease car policy varies from one Trust to another - she needs to check with her HR department and her lease car company. Here's one sample policy from the net (not my organisation) http://www.eastridingofyorkshireccg.nhs.uk/data/uploads/policies/lease-car-policy.pdf
Assuming liability was 100% on the other party, this has little to do with the NHS cover (though presumably they are sorting out any damage to the car). The claim is against the liable party, if traced, or the MIB, as others have said, if untraced. There is very little personal injury cover under any motor insurance.