Car road tax history check - is it possible??

Reason being I've treid to take my reg plate off a car we have owned for 5 weeks as we are trading it in against another car.

The online service said "This registration number cannot be retained online
We need to look into your application further due to the vehicle’s licensing history"

So after calling them they said the car hadn't been taxed and the motor trader had let the previous licence expire.

so why on earth did they not do this when we taxed it 5 weeks ago?

I've checked online and its been Mot'd every year, the milage has gone up on average 9k every year so I'm baffled why us having to apply by post to retain it will be any different to doing it online, its just hindering us.

Is there any resource I can use to check the road tax history of the car?