Home these days is Greenwich and family all in N.Cornwall.
So I have done most of this route over the years in sections, but never done the whole thing in one go
If you wanted to cycle the entire route it is possible to do it all off major roads.
This route also has one major advantage. You are never more than 5 miles from the London/Penzance railway line, so if you run out of time, the weather is against you or you want to skip a boring bit, then just hop on the train!
Greenwich to Hampton Court is on the Thames cycle path that runs along the south bank
Hampton Court to Reading is along the Thames path with deviations onto local roads
Reading to Bath is along the K&A canal
Route then is to Wells, Glastonbury, across the Somerset Levels, I then dropped down to Exeter, across the moor, Tarka trail, then ran parallel with the coast
I used the Sustrans cycle maps as the basis for working out the route supplemented with 1:50 O/S maps for the wider view
I B&B'ed it with B&B's I got from the CTC web site (Cycle friendly B&B's)
Nicest bit was the K&A canal, Devises, Bradford, Bath, Wells
Hardest bit was the final day in Cornwall!
I found 50 miles a day nice and easy, and still gave me time to see stuff
So a week would be fine, or maybe 5 days if you pushed it, I guess the total distance is about 400 miles. (Against 275 miles by car on M3/A303/A30)