Many buildings in London actually have multiple postcodes. In general UK postcodes are granular enough that almost any combination of a name and code should make it, save for situations like several people with identical names living in flats that are fewer than N floors apart.
Postcodes are designed to facilitate sorting and last mile delivery so no surprise if large buildings have multiple codes. DVLA in Swansea has several, probably because they get a lot of post in a few distinct categories.
