I read that there was a plan to have the royal family move to Canada and live here; https://en.wikipedia.org/wiki/Hatley_Park_National_Historic_Site
But surely that wasn't all they had planned.. hell they had plans to rearm germans and invade the soviets.
So what was the plan? Clearly Canada was on their minds as it's the closest thing to British soil as any other country culture wise.
I can't speak for the rest of their planning, but part of the military plan for the Fall of Britain was for as much of the Royal Navy as remained to flee across the Atlantic to Canadian(or in a pinch, American-controlled Icelandic) ports. The Royal Navy still(especially by 1941) vastly outclassed any force the Germans, Italians, or Vichy French could put to sea, so maintaining the Navy in the event of a defeat was a priority. If Britain fell, the only hope of reclaiming it would be American support, and the Royal Navy would be a critical mean of getting across the Atlantic