All good advice above.
SWCP is really easy to access by public transport from London
National Express coaches also go to Barnstaple, Brixham,Torquay, Penzance, Plymouth. though not the speediest way to travel.
Rail also direct to Poole, Dawlish, Teignmouth, Torquay, Plymouth, St Ives, Penzance. Branch lines to Barnstaple and Looe.
If you flew into Bristol there is an hourly bus service from Bristol airport to Plymouth for £24 single.