Garlington Family Genealogy Forum
I was a contributor of English ancestor data to Thesta Scoglands exhaustive Garlington Family History back in the mid 1970s. That section of the book goes into some detail of the name derivation. Basically, the family originated from the Anglo Saxon "tun" (town) whose original chief inhabitant was a fellow by the name of Gyrla (there were no last names at that time; only designations, hence the oldest listed combination name I found was Waleran de (meaning from) Gyrlyngton (Gyrla's tun).
The spelling of the name was pretty varied over the years (formal education being very rare) Gyrlyngton, Girlington, Gerlington, Garlington (all are interrelated as proven by records from the British Museum). Oldest records date back to the North Riding of Yorkshire in 1152 (Waleran)
If you can find the "big orange book" by Thesta Scogland, you would be very lucky indeed. It was a "vanity" publication (meaning we had to pre-pay for its printing, and there were limited numbers. Many major libraries, however, were gifted copies.