Woody Bay was a station on the old Lynton and Barnstaple Railway , a narrow gauge railway line that ran through Exmoor from Barnstaple to Lynton and Lynmouth in North Devon . Woody Bay , within the Exmoor National Park , is a station on the former Lynton and Barnstaple Railway , a narrow gauge line that ran through Exmoor from Barnstaple to Lynton and Lynmouth in North Devon .