From my personal experience, you're wrong at least about Berlin, Prague, Rome, Vienna, Hamburg, Warsaw, Munich, Milan, Brussels, Cologne (man, 100+ thousands of people in the Rhine-Ruhr area don't speak German at conversation level at all) and so on. I don't know about the really eastern ones, but we're talking about the EU, so non-EU Balkan states, Belarus, Russia and Ukraine is excluded. You're probably right about the eastern and eastern-southern border of the EU; it's also true in Poland outside of Poznan, Krakow, Warsaw and several more bigger cities.

Luckily, there is an index we can look at: https://en.wikipedia.org/wiki/EF_English_Proficiency_Index , of course this one received a lot of criticism, so we can look at this one instead: http://www.surveylang.org/media/ExecutivesummaryoftheESLC_21...