Stockport is a city in Van Buren County, Iowa, United States. The population was 272 at the time of the 2020 census. According to the …Stockport is a city in Van Buren County, Iowa, United States. The population was 272 at the time of the 2020 census. According to the United States Census Bureau, the city has a total area of 1.03 square miles, all land.