Rose Uniacke lives in a quiet pocket of West London known for its neat rows of white stuccoed houses and private garden squares. This typical London scene, immortalized in 1990s rom-coms, is suddenly interrupted by Uniacke’s home: a sprawling striped brick house with vast windows.

The house has dominated its corner of the square since it was built in 1860 for James Rannie Swinton, an artist who had become the most fashionable portrait painter of his time. “There’s a story that he was able to ignore the local planning regulations because he was so well connected,” says Uniacke, who moved into the house with her family 15 years ago and runs her eponymous business—which spans interior and furniture design—from a shop nearby. “It’s a mad folly to have been built here when th...