Yes. Some employers already carry out a road risk assessment. But many employers do not, ranging from those with large fleets to small companies with one or two drivers.
The HSE and Department for Transport (DFT) guidance, Driving at work - Managing work-related road safety says: “Some employers believe, incorrectly, that provided they comply with certain road traffic law requirements, eg company vehicles have a valid MOT certificate, and that drivers hold a valid licence, this is enough to ensure the safety of their employees, and others, when they are on the road. However, health and safety law applies to on-the-road work activities as to all work activities, and the risks should be effectively managed within a health and safety management system.”
For more information, see the HSE's road safety web pages. hse.gov.uk/roadsafety