Anglo-Saxon used Runes for their writing system.
Tolkien wrote in Old English several texts of his legendarium, which he (fictionally) attributed to Ælfwine such as the Earliest Annals of Valinor; they were published more recently in The Shaping of Middle-earth and are commented and edited by Christopher Tolkien. These texts have been criticized because Christopher Tolkien did not provide a translation and they remain understandable only by Anglo-Saxon students.
For Lord of the Rings, Tolkien used several Anglo-Saxon names and words, which represented Rohirric, the language of the Rohirrim. This simulated the archaic sense the Hobbits felt with the Rohirrim; Hobbits spoke Hobbitish Westron, represented in the book by English.
However the relation of Old English and English is not the same as with Rohirric and Westron, since the latter descends from Adûnaic, not Rohirric.