Riders Of Rohan - Anglo Saxons?

[Lalwendë]

The linguistic procedure does not imply that the Rohirrim closely resembled the ancient English otherwise, in culture or art, in weapons or modes of warfare, except in a general way due to their circumstances: a simpler and more primitive people living in contact with a higher and more venerable culture, and occupying lands that once had been part of its domain. ~ The Lord of the Rings, Appendix F, On Translation, note 1

What is the 'higher and more venerable culture'? The Romano-Britons? The Celts?