The rail option

The journey can be done by rail in about 36 hours.

Various options from the UK to Sweden, the most plausible involves the Hamburg to Stockholm sleeper. Unfortunately with the current timetable the connections are somewhat tight, but you can perhaps spend a day in Belgium or Germany to spread things out a bit. Times below are for leaving on Monday 6th February 2023, from Deutsche Bahn

1. Take the Caledonian Sleeper from either Fort William or Inverness, leaving early evening. Arrive London Euston about 07.45.
2. Take the 09.01 Eurostar 9116 to Bruxelles Midi, arriving 12.05 (beware that Eurostar currently have a 90 minute check in time, although you may get away with arriving slightly late)
3. Take the 13.25 Thalys 9435 to Koeln Hbf, arriving 15.15
4. Take the 16.04 ICE 1030 to Hamburg Altona, arriving 20.05
5. Take the 21.19 Euronight 346 to Stockholm Central, arriving 09.55

The rail option

The journey can be done by rail in about 36 hours.

Various options from the UK to Sweden, the most plausible involves the Hamburg to Stockholm sleeper. Unfortunately with the current timetable the connections are somewhat tight, but you can perhaps spend a day in Belgium or Germany to spread things out a bit. Times below are for leaving on Monday 6th February 2023, from Deutsche Bahn

1. Take the Caledonian Sleeper from either Fort William or Inverness, leaving early evening. If Inverness, a train from Kyle of Lochalsh adjacent to Skye takes about 2h30, eg Kyle 17.13 to Inverness 19.51. The Inverness sleeper departs 20.45. Arrive London Euston about 07.45.
2. Take the 09.01 Eurostar 9116 to Bruxelles Midi, arriving 12.05 (beware that Eurostar currently have a 90 minute check in time, although you may get away with arriving slightly late)
3. Take the 13.25 Thalys 9435 to Koeln Hbf, arriving 15.15
4. Take the 16.04 ICE 1030 to Hamburg Altona, arriving 20.05
5. Take the 21.19 Euronight 346 to Stockholm Central, arriving 09.55