Juliane Zenke, working for BFI I‘d be either in the cinema (if it was really rainy I would only make it to the Rio around the corner) or in one of the museums or galleries around town. What could make a rainy day in London more enjoyable than looking at Duchamp‘s urinal surrounded by hundreds of tourists at the Tate Modern?
I don't really get homesick, but I enjoy listening to RadioEins and reading Die Zeit, and I call my family and friends back home. It's also nice to make a German breakfast with goat's cheese, fresh bread, a boiled egg and, of course, a milchkaffee.
Notwithstanding the classics, I would go for a mix of Juli Zeh, Benjamin von Stuckrad-Barre, Katharina Hacker, and Roger Willemsen to get a snapshot of contemporary Germany. If these authors haven't been translated, they should be.