Marc is right, I was looking for my supra a year ago when I was 21 and the lowest insurance quote I got was 3500 for an import. Which is why I got my UK spec because I would rather spend the 2500 extra on the car as it was only 1000 to insure it. It is your responsibility to make sure the insurance details are correct even if you provide a reg no as they are not liable for incorrect records at the DVLA.
I found this out when I had my MG ZR 160 which is a 1.8 with VVC but they had it as a 120 which is a 1.8 non VVC, the numbers denote the PS rating so its quite considerable. I only noticed when it came to renewal and I rang them up to tell them about some modifications. Wondered why they were considerably cheaper than anyone else. They wanted to back date my insurance premium which I said wasn't going to happen, they also tried telling me it had had an engine transplant as it was definitely a 120. I knew it hadn't as I had the original bill of receipt, the V5 coo-berated this and the engine number matched.