I don't know but your employee's insurance company might.
Assuming its a passenger vehicle and s/he has normal domestic, leisure and social purposes insurance, s/he is not insured to use the vehicle for business purposes.
This is normally an extension to regular insurance, but it excludes the use of the vehicle for the carriage of goods or samples.
So to do what you suggest and to ensure that everyone has adequate insurance cover, your employee will require additions to his/her motor insurance policy and the cost may be prohibitive.
A cheaper alternative might be a courier van/taxi.