Several ships have served the Royal Navy under the name HMS Integrity.
In addition, the National Maritime Museum database lists three other vessels named Integrity Naval drifters were boats either purpose-built for naval use or commercial fishing drifters requisitioned from private owners.
The Royal Navy primarily used them to maintain and patrol anti-submarine nets.
Lastly, This article includes data released under a Creative Commons Attribution-ShareAlike 3.0 Unported UK: England & Wales Licence, by the National Maritime Museum, as part of the Warship Histories project.