Hi there, a lot will depend on your initial travel plans, such as which airport are you flying into, wil you be transferring from the airport direct to Harwich docks, and if so what time is your plane scheduled to land.
The drive from Heathrow & Gatwick is easily over 2 hours using the M25 'freeway' and that's on a clear run, so you may want to travel the day before you sail.
For lots of thoughts, considerations & options, yuo may find the site London Heathrow To / From Harwich Cruise Terminals
of good use.
If you have any specific dates/times/locations planned then please post them & I'll see what else I can find.