Postcode centroid <-> lat/long has been open data since the initial OS OpenData release. However, if you want detailed polygons rather than centroids, or actual

Postcode centroid <-> lat/long has been open data since the initial OS OpenData release. However, if you want detailed polygons rather than centroids, or actual house number/name data, then this is jealously guarded by Royal F^HMail. The new "OS Open Names" dataset essentially presents the existing datasets in a uniform hierarchy. Think of it as the source data behind an autocomplete geocoder. But it still won't get you the exact lat/long for 27 High Street.