A Department of Transport road list from the beginning of the 21st century describes the A364 as Reserved for North Devon link road. Barnstaple - Bamford, quoting a date in 1972.
"Bamford" here must be a misprint, as it is extremely unlikely that a single number would be allocated to a road between Devon and the Peak District; presumably "Bampton" was meant instead.
The most likely explanation is that the A364 number would be allocated to the new North Devon Link Road between Barnstaple and Bampton,, with the A361 either keeping its old route or being downgraded or rerouted. Presumably the A361 would still have existed west of Barnstaple and east of Bampton.
In the end the A364 number was not used after all. A different route for the North Devon Link Road was constructed in the 1980s via Tiverton to meet the M5 at J27 and this was given the A361 number.