Sounds like a good trip.
I live in Sweden and am getting better at exploiting the perks of DB Sparpreis (Advance purchase) tickets between the UK and Scandinavia on bahn.de
You cannot buy a cheap Sparpreis ticket for the whole journey, or even from London to Oslo, but if you buy a roundtrip with Eurostar then you can get a Sparpreis ticket from either Amsterdam or Brussels as far as Göteborg Central (Gothenburg). these start at €59,90 one way. The trick is to use the additional search options on bahn.de to look for Amsterdam to Göteborg with an overnight stopover in Hamburg. In my opinion Hamburg is a better place for an overnight stop than Copenhagen for the simple reason that hotels (and food, drink, etc) are much cheaper in Germany than Denmark.
If you get the early morning Eurostar from London to Amsterdam, you can get the Berlin train after lunch at 14:00 or 15:00 and be in Hamburg with one change by around 19:00. Stay overnight in Hamburg (lots of hotels starting at €50) then get the first Copenhagen train around 08:00. You can be in Gothenburg by early evening, all on the same ticket.
(Obviously all of this is speculative if you use an Interrail ticket, but it may be tempting for you or other people here)