Car cloning is a very unpleasant experience. The victim is usually unaware of the crime until a parking ticket or speeding fine lands at their door. The police will be unaware of the cloning situation. They should have images of the offending vehicle, which may end the case (as the car may be of a different make, model or colour to the one you own). If the police require further information, include details of your car's local movements and any distinguishing features it may have (like a bumper or window sticker). Hopefully, the authorities will catch the offender.

In regards to the number plates, has the DVLA issued a new registration number for the car? If not, you can continue to use the existing ones. However, if you have a new reg number, there are many highstreet companies - like Halfords- that can provide this service for you.