As has already been explained, the original issue is that the plates you put on your vehicle did not correspond to the VRM on your insurance policy - so on the face of it (on the assumption that the VRM on the plates was correct) the vehicle was not insured (or more precisely not insured for you to drive it).
You have not been charged with any offence yet and cannot be charged until the expiration of the 28 days you were given to accept the COFP.
However, if you were to be charged with driving some vehicle identified by the erroneous VRM, a letter from your insurer stating that you were insured to drive that vehicle would be very helpful as evidence that you were insured to drive that vehicle.
As the redacted COFP (with pretty much the only relevant detail - the VRM - having been redacted) apparently refers to the correct VRM, and the one which is stated on your insurance certificate, if any subsequent charge of driving without insurance identifies the vehicle by that VRM - in other words if you are accused of driving without insurance in what is identified by the charge as the vehicle that you have a policy insuring you to drive, then such a letter is irrelevant.
There is no "correct" way to contact the police, phone them, write to them, send a carrier pigeon. If you can't get any sense out of the reporting officer, try speaking to his sergeant or inspector to review the matter.
