It is quite normal practice for employees to be reimbursed at a reasonable mileage rate for business use of their own vehicles.
A statutory system of Approved Mileage Allowance Payments (AMAPs) applies for employees using their own vehicles for business journeys, as follows:
Unless the employee is reimbursed at a rate higher than the AMAP, the payments do not need to be reported on a P11D. If the employer pays less than these rates, it is possible for the employee to claim income tax relief for the shortfall.
Rates of up to 5p per mile, per passenger, are also tax and NICs free when paid for the carriage of fellow employees on the same business trip. This now covers volunteers who drive for hospital car services etc, even though they are not strictly employees.