Do it online?????
Oh shoot you can't without the reference number on the reminder or V5, if i were you i'd call the DVLA and see if there's any way you can get the number over the phone.
The worst you will get done for would be failure to display a tax disc, and there's no way on earth youd ever get caught, if you tax it online it will be registered on the ANPR as being taxed anyway.