Ive had a similar experience when registering a change of car (but not number plate) for the Dartford Crossing.
Registering always shows the old car but a phone call soon rectifies this. I have been told each time that the make of car is of little importance, they are only really interested in the registration number.
Of course, this would be a different matter where emissions are involved (CAZ) but as long as you know your vehicle complies I doubt that there would be a problem.
I cannot imagine that the authorities cross-check every make and model. More likely, the authority would use the database information it had available and, if the 'old' car complied, the reg number would continue to be accepted.
As long as you know the new car complies and the registration number has been transferred correctly then it is hardly your fault if their database has not been updated.