I've recently written a paper that examined the impact of the horse in the 19th century, particularly with a focus on how it was impacted by the introduction of the steam engine.

Having said that though, the car did not overtake the horse in the course of a night, from what I've read it was a slow progression over time and the horse population of England did not have a significant drop until post world war one. I do have some sources that might be beneficial to you if you can access them.

theres an article titled “Transport” in a book called The English Urban Landscape, compiled by Phillip Walker. The article itself is by John Armstrong, and it covers carriages, the introduction of trams, as well as the early automobile.

Also of possible use is "Victorian England: The Horse Drawn Society" by F.M.L. Thompson. As the title says, it focuses primarily on the horse but does make mention of the rise of the automobile.