This is a bit difficult to parse, particularly without some context (I have never read Seven English Cities, so I can't really say why the Americans are connected to their luggage by their heart-strings, for example); however, I think this is what it's trying to say:
These (the Americans who were whirred awayprepared their spirits for adjustment to London by the impatient expresses (trains)novel conditions) the successive trains carry into the heart of the land everywhere, these (the same Americans) and their baggage, to which they (the same Americans) continue to be attached by their very heart-strings...
Perhaps the clearest way to phrase it would be, if you'll allow the fancy writing to be replaced by more plain description:
The Americans were whirred away, who after arriving took some time to London by the impatient trainsadjust to their novel conditions, were carried into the heart of the land everywhere by the trains. These Americans continued to be attached to their luggage by their very heart-strings, which invisibly stretched from their first-class corridor compartments to the different luggage-vans.
(Edited based on @KateBunting's observations)