From Barnstaple train to Exeter St. Davids, train to London Paddington, then train to Heathrow Terminal 1. 4hrs 26min £68. From Barnstaple, Bus Station bus to South Molton, The Square, line 155 bus to Tiverton, Bus Station, bus to Hammersmith Bus Station, bus to Hounslow Bus Station, then line 111 bus to Heathrow Central Bus Station. 7hrs 16min £51. From Barnstaple drive to London Heathrow. 3hrs 36min £41.