Well, Edward VII wasn't a Hanoverian. Hanover had a semi-Salic succession, which meant that when Edward's mother, Queen Victoria, became queen in 1837 the Hanoverian throne passed to her uncle the Duke of Cumberland (aka Ernest Augustus, king of Hanover) and the personal union of the British and Hanoverian monarchy was dissolved. So Edward inherited his father Albert's house.

I've written about the Hanoverians a couple times:

https://www.reddit.com/r/AskHistorians/comments/3jbpyk/britains_role_in_running_hannover/

and:

https://www.reddit.com/r/AskHistorians/comments/401lb1/why_wasnt_hanover_incorporated_into_the_uk/

if that's useful.