The election takes a month.
Transfer of power is overnight.
The king accepts Rishi's resignation as a formality and invites Starmer to form a new government, again as a formality.
Some call our constitution clunky and old-fashioned. But it works well enough. And after Magna Carta (1215 AD) and the regicide (1649 AD), everyone, including the king, is subject to the law!
Sometimes an overmighty king needs to be executed!!! This has been said in England since the twelfth century.