Very interesting. You are on to something - I am using Europe as shorthand for Western Europe. When I speak of Eastern Europe I always add Eastern. Just like when I speak of [North] America versus South America or [West] Germany vs East Germany.
However I would say this type of shorthand is far more widespread than UK and Scandinavia. My German friends adds Eastern Europe when speaking of Ukraine, too, as does my Italian friends.
The cultural differences in Europe are far more complex than an East-West divide. Saying that Ukraine has a European culture is like saying India and Japan have "Asian" cultures. It sure doesn't make them the same and frankly, it does not even very similar.
However I would say this type of shorthand is far more widespread than UK and Scandinavia. My German friends adds Eastern Europe when speaking of Ukraine, too, as does my Italian friends.
The cultural differences in Europe are far more complex than an East-West divide. Saying that Ukraine has a European culture is like saying India and Japan have "Asian" cultures. It sure doesn't make them the same and frankly, it does not even very similar.