A note saying it was in the post is usless. It's all recorded on computer so a quick check by a traffic cop / warden would reveal this however, there is also the offence of 'failing to display a valid tax disc'
from the DVLA website:
A current tax disc must be displayed on the vehicle it was bought for. If you buy a new tax disc before your current tax disc expires, you should not display the new one until the old one has expired. The new tax disc is only valid from the first day of the month you have taxed from. The maximum penalty for failure to display a current tax disc is £200. The tax disc can not be transferred between vehicles.