Those vehicles listed are not exempt from displaying a road tax disc. They are required to license annually and to display a 'nil' or free VED disc.
Prior to the enactment of the Vehicle Excise and Registration Act (VERA) 1994, which updated and consolidated the old road tax statutes, there were debates about the VER Bill in which it was proposed that police vehicles used for specific duties (I don't know which duties were specified) be included on the exemption list. No amendment was made to the Bill in respect of this.
Presumably the proportion of police vehicle usage for emergencies as opposed to everyday policing is not significant enough to warrant the inclusion.