Heathrow to Southend
As someone who has often done this drive at all times of the day, it usually takes 1 hour 40 minutes. This is junction 14 of M25 going round the northern section until the A127. (forget going southerly as if blockage on the QE2 crossing you are in trouble).
Have done it in less than this in the early hours of the morning, and around 2 hours in busier times.
Southend ATC very pleasant and helpful all hours of the day and night.