From Barnstaple train to Exeter St. Davids, train to London Paddington, then train to Heathrow Terminal 1. 4hrs 20min £71. From Barnstaple, Bus Station line 118 bus to Okehampton, Martins, bus to Exeter City Centre, Bus Station, then bus to Heathrow Central Bus Station. 6hrs 55min £41. From Barnstaple, Bus Station bus to South Molton, The Square, line 155 bus to Tiverton, Bus Station, bus to Hammersmith (Dist&Picc Line) Underground Station, then Tube to Heathrow Terminals 1-2-3 Underground Station. 6hrs 45min £40. From Barnstaple drive to London Heathrow. 3hrs 36min £41.