What it takes for a Normal Civilian Joe to get a Driving License:
Apply to the DVLA to get Provisional License
Apply and do lessons (normally about 20 to 30 1 hour lessons is the average)
Apply and do Theory Test (about 50 Qs from Highway Code and 5 Hazard Perception Tests)
Apply and do Practical Test (45 mins)
Pass
Never get examined or tested again unless you do C1/D1 or motorcycle.
What it takes for a Brand New PC straight out of training school to get a Police Driving Licence Level 1
From the lowest Level 4 (AKA Basic or Panda)
Wait at least 18 months from date of start before you can even ask to do Level 4 Driving
Gingerly ask your Sergeant then Inspector if you can do it
Apply for Level 4 Driving to your Safer Driving Manager (SDM)
Pass Eyesight test (much higher standard than normal DVLA requirements)
Apply and Do Police Driving Theory Test (includes Normal Highway Code, Police Driving regulations and Signs, the Police also like this system where you cant get less than 75% in a single part of the exam so you can do real excellent in Highway Code and Signs getting an overall pass mark of 90% but flop in Regulations getting only 70%, this will mean you FAIL)
Apply and Do a Police practical driving assessment
Pass - You can now driving a Police Car like a normal car except you can use the lights to stop traffic or block a road but cannot use the lights and two tones to respond to an emergency. You will also have to show your Normal DVLA License every 1 year to make sure you have no points on it.
From Level 3 (IRV or Incident Response Vehicle)
Wait at least 12 months from date you passed your Level 4
Gingerly ask your Sergeant then Inspector if you can do it
Apply for Level 3 Driving to your SDM
Pass Eyesight test
Apply and Do Police Driving Theory Test (includes Normal Highway Code, Police Driving regulations, Signs, additionally read and learn everything from a book called ROADCRAFT which goes into detail of advanced driving techniques (also know as 160 pages of mind numbing revision))
Apply and Do a Police practical driving assessment
Be selected for an IRV course, spend 2 weeks at driving school learning and pass a final drive, at anytime you could be told you are not fit for IRV and returned to your station.
Pass - you can now use the blue lights and two tones to respond to incidents as well as using the car normally
HOWEVER 3 months after passing you must be assessed again to make sure you remembered the stuff and every 3 years you are assessed again.
For Level 2 and Level 1 (this is combined as most forces combine the two courses together, also called Advanced or RT Driver)
Be selected for Level 1 Advance RT Driver (you get picked by managers not by applying)
Some forces require you pass a DVLA C1/D1 course first as well
Pass Eyesight test
Apply and Do Police Driving Theory Test (includes all the above stated yet has more abstract questions from ROADCRAFT meaning that you can't use straight forward answers)
Apply and Do a Police practical driving assessment
Spend 4 weeks at driving school learning and pass 2 final drives, this is a very intense, pressured and stressed course, failure rate is high.
Pass - As above to Level 3 but now you can drive even more powerful Police Cars and are specially trained in tactical pursuit management
Again 3 months after passing you must be assessed again to make sure you remembered the stuff and every 3 years you are assessed again.
Remember Police Officers who drive are held accountable to the standard and manner of driving, each police car carries a blackbox like device so officers never lie about a collision, officers are very aware of their speed, the condition of the roads and traffic and the condition of the vehicle they are driving. As you can see from above officers not only have to do a lot of reading, go on a lot of courses, get continually assessed and once they have passed a level are continually assessed, any involved in a collision or have a poor standard of driving can have their police driving revoked at anytime by managers.
So think about the amount of training, lessons, assessments and driving experience you have had and the amount the Officer has to do? It can take an officer around 10 years to go from nothing to Level 1, most never even get passed Level 2 let alone 1.
Whilst correct that police cars have a lot of distracting IT equipment such as radios, computers, PDAs etc, most of the time response police cars (that's level 3 to 1) have a driver who Drives and an operator who manages all the other stuff, whilst driving at speed the driver will not touch any of the IT kit and leave that up to his operator.
People who freak out when the police approach behind them are either not paying attention to their mirrors or inexperienced drivers