I have been reading a steam-punk novel called The Affinity Bridge by George Mann. It is not great literature, but the imagery is good. One of the plot strands revolves around mechanized men, termed 'automatons' - note, not robots. That reminded me of a Father Brown story in which there was a shop full of automatons. In The Man Who Was Thursday there are episodes reminiscent of steam-punk. In one chapter, a secret policeman is sitting down at a table in a tavern, when the whole table descends into an underground system of tunnels. Even without this science fiction stuff, the Edwardian era, when, I guess, Chesterton wrote much of the best stuff, was one in which there was an interesting mix of old, traditional technology, and new, exciting technology. For example, in TMWWT, Symes sprints to catch an omnibus to escape an anarchist pursuer. The book does not say, but presumably this was a new-fangled, diesel-powered omnibus, because he would hardly need to sprint to catch a horse-drawn omnibus. However, a day or two later, Symes is obliged to fight another anarchist in a duel with a sword. In The Affinity Bridge I was slightly confused because the period seemed to be Edwardian, but Queen Victoria was still on the throne. This puzzle was resolved when we find out Queen Victoria is being kept alive by an artificial respirator, so the period was Edwardian. Previously, I assumed steam-punk was inspired by late 19th and early 20th century science fiction writers such as Jules Verne and H.G. Wells, but maybe G.K. Chesterton should be on that list too.
Edit: the Father Brown story with the automations was called The Invisible Man