By road it takes around 2.5 hours between Heathrow and Harwich, but you should allow an extra hour or so, in case of delays on the motorways.
The cruise terminal at Harwich is several miles outside Harwich the town, in the middle of the international port:-
Harwich International Port
Tel +44 (0)1255 242000
It is popular with passengers going to the continent especially Holland or Denmark.
For a carefree airport transfer click here