Norway had always been a factor of interest during the war  for both parties, and especially for United Kingdom and Germany. They fought there in 1939.

Norway is a large, open-on-the-sea coast on the Atlantic Ocean and it provided a good path for German submarines. It also helped them secure iron supply from Sweden.

The British did consider actions against Norway, and applied some such as the Commando actions in Lofoten and Vägso. It led the Germans to concentrate more defensive troops there, and this hampered further Allied actions.

That is for the general picture. The fight in Mediterranean Sea became pregnant and British engaged there rather than in Norway (or at the same time as Norway) because they had already difficulties in convincing Americans into engaging in the Mediterranean peipherical sea.

About the specific intervention to prevent or act as spare in case of a Russian collapse, well, besides the logistic and strategic difficulties, it had an issue: if Allies engage firmly in Norway, it will be far from the English coasts and far from English-hold Egypt: thus, adding to the defense of those two points, they would have to attack on a difficult ground: not a great idea.


About the specific Allied feeling about the plan, you should note it was at first Churchill's idea. But the Italy idea was one as well, so I suspect that Churchill truly wanted peripheric operations and eventually got one for abandonning the others. The Americano-Canadian Special Forces, who should have fought in Norway, ended up in Italy.