Stuttgart is a major transport hub in Germany, and there is a regular train service from London St. Pancras Station. By traveling first to Bruxelles, then via Frankfurt, the journey can take as little as 7 hours. The main rail provider along this route is Deutsche Bahn, which operates two services each day.
Stuttgart combines breathtaking architecture, incredible natural beauty and a vibrant nightlife, and has consistently been voted one of the continent's most liveable places. Stuttgart is renowned for its high quality wine, and enthusiasts can visit vineyards along the picturesque Neckar river and sample some of the excellent local produce. Traditional architecture abounds in Stuttgart, with sites like the Old State Gallery and the Opera house still enormously popular, though the Mercedes Benz Museum, with its contemporary design and double helix interior is equally as impressive. Offering guided audio tours in a range of languages, it provides a complete history of one of the world's most recognisable and popular cars.
Here are some other resources that might have the information you need