Only currently, due to lack of requirement. Don't forget the good old Vulcan.however Europe has not a single strategic bomber
And don't forget that within the "all-out war" there would have been e.g. German Tornado IDS with tactical nukes going almost ferry range (i.e. 3000 km with maneuvers) to their target. Yes, they trained for that kind of scenario. France and the UK don't need bombers for strategic projection. That's what nuke-tipped SLBMs are for.
As for European ASW capability, any Russian sub not in the Northern Fleet is of no importance to Europe (i.e. about half the sub fleet). Any Russian submarine that wants to threaten anything in Europe needs to go through the Norway-UK-Iceland gap. Which is heavily cordoned off by NATO SMNG ASW forces and MPAs from all sides.