In September 1894, the Prime Minister of the United Kingdom was in London to ask Vastra, Jenny Flint, and Strax to protect a time machine at the Academy of Science. Strax mistook him for a woman. (PROSE: The Singular Case of the Time Machine)
Behind the scenes
Although it is not stated in the story, Archibald Primrose, 5th Earl of Rosebery was Prime Minister at the time.