Ex police car

I have just bought a car that was an ex police car and found that, interestingly enough, that they do not have to be taxed and thus do not require MOT certificates. That meant that to tax the car I had to go to the local vehicle licensing centre. That was quite a simple task as you needed all the documents as usual but needed to complete a form or two. one form was for licensing and the other form was for classifying the vehicle.it would have been useful if I hadn't posted the new owner form on the log book, as they would have processed the change of class there and then. However, I will still receive a new log book one for the change of owner and one with the change of classification from police to diesel. The car also needed an MOT, so the dealer put that on for me as I would need it for the tax on the car.
I would like to know if the car as police car was insured with them as I seem to believe that government cars are self insured, with funds put aside. Apparently that's more cost effective.
They would obviously need to be third party insured for other drivers incidents, but I will continue to look out for this information.
This car was a Ford Mondeo diesel 1900 130. I used to own one of these a few years ago, but when I test drove this car the power is amazing. Its the 130 bit meaning 130 BHP, the other car I used to have was a 115 BHP and therefore as suspected those police cars always have something done to them to make them fast.