Police, other 'Public Safety' workers and drivers who have a 'Push To Talk' facility to communicate are allowed to do such whilst driving. Surprisingly it also includes Radio Ameteurs.
Whether or not that will change when the Emergency Services Network is finally operational I wouldn't like to say. The ESN is reliant on the EE 4G network and will use what are effectively modified mobile phones. The present PS radio kit whilst looking like a big mobile phone is primarily PTT operation but can act as a mobile phone.