Wim,
Can't help with the Harwich end of your route, but when I go to Cornwall, I take the A30 from the Basingstoke area. If you need to make up time, it would have to be M4, M5, A30. Or A303 all the way to Exeter.
The A30 is twistier and slower than the A 303, and noticeably quieter.
The A30 goes through Salisbury, Shaftesbury, Sherborne and Yeovil. On reaching the M5 junction near Exeter you basically have 3 choices:
1. Stay A30 which is becomes mostly dual carriageway well into west Cornwall.
2. Take the A38 (dual carriageway) south of Dartmoor, via Plymouth. Slightly more scenic.
3. If the weather is nice, take the B3212 off the A 30 over Dartmoor. Utterly brilliant scenery. At Two Bridges, right in the middle of the moor, take the B3357 through Tavistock, then A390 to Liskeard, and back on to the A38.
Good maps available at:
http://getamap.ordnancesurvey.co.uk/getamap/frames.htm
or:
http://www.a-zmaps.co.uk/
Let me know when you are going!