Trains from Gothenburg are available from the UK, however a number of changeovers are required. Departing from St. Pancras International you will first take a Eurostar train to Paris. There are five journeys between London and Paris a day with the final train of the day departing at around 5:30PM. From Paris you will travel to Hamburg via a Deutsche Bahn train service, the journey will include two stopovers via Frankfurt and Hannover and should take around 8.5 hours in total. From Hamburg you are able to complete your journey into Gothenburg via a further stopover at Copenhagen international train station. The final leg of your journey should take around 8 hours to complete. Gothenburg Railway station is the main rail terminus in the city and services around 30 million travellers every year. Located centrally the station offers excellent travel links around the city and is positioned conveniently near to both bus and taxi depots.
Gothenburg is renowned for its incredible quality of life, clean streets, welcoming locals and beautiful natural landscapes. One of the five largest Nordic city's, Gothenburg is home to some of Sweden's most respected educational establishments, art galleries and museums as well as a vibrant and buzzing nightlife scene. Most of what's great about Gothenburg is based around waterside activities. With close to 25,000 boats and yachts dotted around the cities various harbours, life tends to centre around the water. Visitors can sail, wind surf, water ski and swim in the crystal clear water before drying off in one of the city's numerous waterside bars, restaurants and pubs. All this combined with the relaxed pace of life and friendly, safe atmosphere make Gothenburg a truly wonderful place to visit.
Here are some other resources that might have the information you need