I’m headed to Gothenburg in a couple of weeks. Hamburg is as far as you can get in a day from London. Brussels, Cologne are the intermediates. I’m not sure I’d want to go all that way on a single train. It’s nicer to get off for an hour or two, have a wander, grab some food, then do another leg. That said, on first look, going direct to Cologne gets you one step closer to lots of Germany. And perhaps if the Aachen bypass line were built that could give you a journey time around 3.5hrs.
However, Jon Worth’s report rules out the Hbf as impractical for an international terminal. I’m not sure if another Cologne station gives you the same onward connectivity options and I doubt Cologne is a big enough market on its own.
Anyway, say a solution were found for Cologne then you add 4hrs to Hamburg and all in all that’s relatively painless for the distance travelled.
Hamburg -> Copenhagen is currently a direct train in 5hrs and onwards to Gothenburg is another 3.5hrs. Which on its own isn’t too bad. Once Fehrmann is open and the German line upgraded, I think the time to Copenhagen drops to around 2.5hrs? With further improvements to the west coast line in Sweden and perhaps if the Oresundstag were to venture down to Hamburg, you could plausibly see direct trains in 6hrs. Especially because the Danes have done precisely what would apparently be economic suicide for the Belgians and built a bypass of Copenhagen central station.