Despite living relatively nearby, I have just recently learnt about Pilning station. That I have been unaware of it until now is not particularly surprising, as there are only two services a week. (it attracted some news coverage as the second service is being moved an hour earlier, making the schedule even less useful).
Further, these are not comprised of an inbound and outbound pair (say, one train to Bristol and one back)- instead, they both run in the same direction, east. This is because the westbound platform was rendered inaccessible by the removal of the passenger footbridge. Is Pilning unique in this regard, at least within the context of British railways?
Clearly any station which features only a single service a day would be another example. But conceivably there may be others with more regular service, yet still just in one direction (maybe some sort of loop arrangement, or due to a similar loss of a platform). @Berend points out the obvious case of a terminal station; I'd like to exclude those from consideration.