Just to update this:
Car was sold - buyer knocked off £100 to replace the plates (yes I was honest and told them, gave them the crime ref number etc. would have felt bad if they got pulled over and ended up with no easy way to prove the car was legit).
Finally managed to speak to Warwickshire police and they reviewed all the evidence and accepted it was cloned - never saw a picture of the other car but they did say there were some differences to the photos we provided.
West Midlands Police also finally sent us a letter saying they'd reviewed the evidence and were happy it wasn't our car.
The parking company responded saying that as we told them my partner was neither the driver or registered keeper of the vehicle in question, they couldn't communicate with us due to data protection. Sent them a rather sternly worded email pointing out that since they had now accepted that my partner was NOT the registered keeper, they had no further reason to communicate with us, but we would be more than happy to assist with their investigation for a very reasonable daily fee. Got a response a few days later dropping the matter.
So, all resolved, but a real pain in the **** and costs us £100 (plus the time and effort collecting the evidence and sending it off etc.)