For an interesting train journey, go by rail from London to Brussels on Eurostar, then overnight to Hamburg. The trains are lovely and new, and even have showers.
Next day, press on to Copenhagen by train and boat - the train drives onto the ferry between Puttgarden and Rodby. After that, it's over the Oresund Bridge to Malmo!
Book tickets through Ffestiniog Travel, who will hold the reservation for a few days so you have time to sort out your other arrangements! For those food emergencies, I recommend taking Ryvitas and a jar of peanut butter - no refrigeration required!
Updates
You could also take the Eurostar to Brussels, then Thalys train to Cologne (Koln) then overnight from Cologne to Copenhagen and over the bridge to Malmo. Leave London around 2.30pm and be in Malmo by 11am the next morning.
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