One possibility is that he was already familure with the linguistic history of Anglo Saxon, and therefore he would not have to create something totally new and in depth for the Rohirric history contained in the appendixes (you will note when reading of the early Rhovanion kings that the names all have their roots in Germanic Gothic, an early relation of Anglo Saxon). The other reason could perhaps be a bit of a subtle "political" hint on his part.
Although a South African by birth, Tolkien in his letters shows his obvious preference for the Warwickshire area (he was even married in Warwick). Early writtings of Tol Eressa in the Lost Tales clearly show that Warwick was the capital city. Although this idea was abandoned, it played over in his Rohirric culture. The Warwickshire area was within the Mercian provence of Anglo Saxon England, and the Rohirric language as exhibited in the books are in the Mercian dialect - a specialtiy of Tolkien. Well, we can allow the great man his little follies - and it's really quite an interesting story.
True Rohirric is akin, as hinted in Theoden's talk with Merry, to the true Hobbit (Tolkien name: "Kuduk") tongue, which in retrospect makes sense, as both cultures owed a large portion of their development by the banks of the Anduin.
These are the only known words of true (not Anglo-Saxon) Rohirric -
kastu (treasure, mathom)
trahan (burrow)
k�d-d�kan (hole-dweller, Hobbit)
loho-, l�- (horse, the �o- part in e.g. �owyn)
Loth�r (horse-folk, �oth�od)
L�grad (Rohan, O.E. �o-marc, Horse-mark)
t�rac (king, name of Theoden)
r�g, pl. r�gin ("wild man", Wose)
