In 1870-72, John Marius Wilson's Imperial Gazetteer of England and Wales described Fair Oak like this:
FAIROAK, a chapelry in Bishopstoke parish, Hants; 7 miles S of Winchester. It has a post office under Southampton. The living is annexed to Bishopstoke.
GB Historical GIS / University of Portsmouth, History of Fair Oak, in Eastleigh and Hampshire | Map and description, A Vision of Britain through Time.
Date accessed: 27th March 2017
Click here for more detailed advice on finding places within A Vision of Britain through Time , and maybe some references to other places called " Fair Oak ".