@SK53 and @Russkel really answered this in the comments of the other proposed answer, but for clarity, the approximate explanation/answer is as follows:
- Nominatim is based on the OSM data
- OSM Post Code data is largely incomplete
- The current status of Post Code data can be viewed on the [OSM TagInfo][1] website.
- Currently, if a Post Code is added to a Nominatim Query and the Post Code is not within the OSM data set, Nominatim will return **no results**
This appears to be the intended behaviour, which I believe to be wrong and have raised as an issue on Nominatim.
[Issue on Twain's Nominatim Github Repo](https://github.com/twain47/Nominatim/issues/59)
OSM Trac](https://trac.openstreetmap.org/ticket/4867)
[Issue on OSM Trac](https://trac.openstreetmap.org/ticket/4867)
Nominatim Github](https://github.com/twain47/Nominatim/issues/59)
[1]: http://taginfo.openstreetmap.org.uk/keys/addr%3Apostcode#overview
[2]: https://github.com/twain47/Nominatim