And quite often Amazon will even ship within Europe. Many articles on Amazon UK have a note that delivery will take 2-3 days instead of 1 day, which is always a sign that they ship it from a warehouse somewhere else in Europe (mostly Germany).
And this seems to work for FBA articles as well. But they can handle that due to their own logistic network. Parcels within Europe are still rather expensive, compared to a domestic Parcel. I can still send articles much cheaper from London to Inverness (Scotland) than to Brussels, even though Brussels is closer.
But that's probably just a function of the low B2C trade across borders, which leads to a sparse delivery network.