Forget about starting at Exmouth as you will be just walking up an estuary.
If you want to get to north Devon from Heathrow - use the Railair bus link to Reading & then catch a train that is going to Taunton. From Taunton, take a bus to Minehead for your first night - or spend your first night in Taunton. You then start walking west from Minehead along the South West Coast Path in the Exmoor National Park. Beware that the north Devon Coast does involve some steep sections. Make a note of where the main towns/villages are en-route. When you get to Lynmouth, you can, should you wish, curtail your walk and take a bus to Barnstaple. Alternatively, continue heading west. Either way, you will have to end up in Barnstaple in order to catch a train back to Exeter (worth a look) and then another train to Totnes.
Alternatively, take a train from Reading to Exeter and change for one to Barnstaple; then take a bus to Bideford & start walking west from there. (This coast is different to the bit west of Minehead).
https://www.firstgreatwestern.co.uk (Advance booking get cheaper fares. You may wish to book a return Reading to TAU and when you wish to leave Totnes, buy a single as far as TAU).
http://www.traveline.info (for buses).
Check landscape on Google Earth.