The police: "the civil force of a state, responsible for the prevention and detection of crime and the maintenance of public order."
If you gave this task to "transportation department or some such" they become the police. They become the civil force of a state, responsible for the prevention and detection of this specific crime.
Except of course if you boot up a brand new police force just for this task they will bumble around and make all the mistakes while they lean how to you know police.
> a lot of the privacy concerns rightfully stoked by involving the police
What privacy concerns does this raise which are not already raised by the 11,000 other automatic number plate recognition cameras in operation in the UK?
The Police are already tooled up to issue traffic citations. Tooling up the BTP to do the same task would just mean more money, and end you at the same result, no?