Downton, Herefordshire. Downton is a civil parish in Herefordshire, located in the north of the county and containing the village of Downton-on-the-Rock. It is part of the Leintwardine group of parishes and shares a parish council with Leintwardine and Burrington. In the Domesday Book Downton is referred to as Duntune, meaning hill settlement. At Downton Gorge the River Teme cuts through a limestone ridge; above the gorge is Downton Castle, an 18th-century country house with a tower built to resemble a castle.