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.
A Vision of Britain through Time includes a large library of local statistics for administrative units. For the best overall sense of how the area containing Fair Oak has changed, please see our redistricted information for the modern district of Eastleigh. More detailed statistical data are available under Units and statistics, which includes both administrative units covering Fair Oak and units named after it.
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: 03rd May 2016
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".