Old English
From Tolkien Gateway
Old English (sometimes called Anglo-Saxon, though Tolkien disliked the term) was the ancestor language of modern English. It was also the mother language of characters Ælfwine and Eriol.
History
Tolkien was a professor of Anglo-Saxon at at Pembroke College from 1925 to 1945. He was strongly influenced by Old English literature such as Beowulf and favoured especially the Mercian dialect. Tolkien wrote in Old English several texts of his legendarium, which he (fictionally) attributed to Ælfwine.
Rohirric
For Lord of the Rings, Tolkien used several Anglo-Saxon names and words, which represented Rohirric, the language of the Rohirrim.