If it's a used shell, which it most likely is, then putting the ID off another car on it would be ringing it technically, which is obviously against the law. Though it is very common in rally circles to be honest.

It's that or a Q plate I should think. Some people don't like Q plates, as it seems to have a bit of a stigma to it, but it does have good points. Lack of a proper emissions test come MOT time for one!