I don't think horseradish sauce is an English dish as such anyway.
History
Horseradish has been cultivated since antiquity. According to Greek mythology, the Delphic Oracle told Apollo that the horseradish was worth its weight in gold. Horseradish was known in Egypt in 1500 BC and has traditionally been used by Jews from eastern Europe in Passover Seders, often representing maror. Cato discusses the plant in his treatises on agriculture, and a mural in Pompeii showing the plant has survived until today. Horseradish is probably the plant mentioned by Pliny the Elder in his Natural History under the name of Amoracia, and recommended by him for its medicinal qualities, and possibly the Wild Radish, or raphanos agrios of the Greeks.
Both root and leaves were used as a medicine during the Middle Ages and the root was used as a condiment on meats in Germany, Scandinavia, and Britain. It was taken to North America during Colonial times.