The kingdom of Hanover was it's own independent state, through it was part of the German Confederation (Meaning that theoretically, they could have become truly independent of its German neighbours) and was ruled in a personal union with the United Kingdom, meaning the ruling monarch held the position of ruler in both nations but that aside from that they were independent states with their own laws, institutions, foreign policy, domestic policy, languages etc.

British law held no sway in Hanover, Hanoverian law held no sway in the UK. English was spoken in the UK, German in Hanover, English had no official status in Hanover and German had no official status in the UK. The UK parliament held no sway in Hanover, the Hanoverian court held no sway in the UK. They were separate nations besides there ruler, that is why Hanover was not counted as part of the British Empire.