Author D. H. Lawrence lived in many places around the world-- including Germany, Italy, Australia, Mexico and New Mexico--but his short story, "The Rocking-Horse Winner" takes place in his native England. Lawrence lived much of his life in Croydon, south of London, and this could be the setting of the story.
They lived in a pleasant house, with a garden, and they had discreet servants, and felt themselves superior to anyone in the neighbourhood.
Oscar spends time with Bassett and Paul in Richmond Park (London's largest royal park); Paul hopes to attend his father's alma mater at Eton College; Uncle Oscar has a home in Hampshire on the southern coast of England; and one of the big races in the story is at the Lincoln Racecourse, home of the Lincoln Handicap. First published in 1926, "The Rocking-Horse Winner" probably is set in the early- to mid-1920s, and certainly after the invention of the automobile, since Uncle Oscar often took Paul "for a ride in the car."