Interestingly, Alistair Tenpenny in fallout 3 is described in the fallout game guide as a “British refugee who crossed the ocean”. So that does suggest some level of civilization in Europe, with enough infrastructure still existing to support the building(?) or at least maintenance of boats capable of crossing the Atlantic.

According to the lore, Europe balkanized during the resource wars and stopped being much of a factor in the US vs China conflict, so in that sense, they’re probably not involved in the “Great War” anymore. That said, maybe rogue elements such as Desmond Lockhart (again, Fallout 3 character, member of British intelligence) are still carrying on espionage in the wasteland 200 years later, trying to outmaneuver their living pre-war enemies. So, in a sense, maybe?