According to GOV.UK, employees may be excluded in specific circumstances if they use the fuel in one of the following ways:
Cars used for business purposes only
Any journey an employee makes as part of their job duties can be considered a business purposes journey, for example, a salesperson travelling to visit a customer. An employee's commute to a temporary workplace is also taken into consideration. You must instruct your employee not to use the vehicle for personal travel and ensure that they don't in order to qualify for an exemption.
Cars used for employees with a disability
Cars modified for disabled employees may be excluded if they are only used privately for trips between the employee's home and place of employment or when the employee is going to work-related training.
When the employees pay their own fuel
Employees do not have to declare or pay a fuel tax if they purchase their own diesel or petrol or reimburse the employer for the fuel they consumed during the tax year.
You don't pay fuel tax on Pool cars, which are shared company vehicles stored on the grounds and exclusively utilised for business purposes. However, you will be charged if a pool car is used for personal use or is shared by employees and is not a pool car.
Cars provided to close relatives
You do not have to pay anything if you're an individual employer (e.g. sole trader) or if you offer the vehicle to someone who works in your business, but only as they are a close family, not because they are an employee of your company (e.g. you give your child a car as a gift). Included in the definition of a close relative are your spouse, civil partner, parents, and any additional dependents or home guests.