Wantage

... is in Oxfordshire now, but prior to 1974 it was in Berkshire.

Did Berkshire exist in Alfred the Great's day (c. 848 to 899)?

Wikipedia talks about "historic counties", which were established by the Normans. It goes on to explain that it was the Romans who first divided Britain up into administrative areas; before their arrival "there were distinct tribal areas, but they were in a constant state of flux as territory was gained and lost. After the demise of Roman Britain around 410 these first divisions of land were generally abandoned ... The areas that would later form the English counties started to take shape soon afterwards ... In southern England ... shires emerged from earlier sub–kingdoms as part of the administrative structure of Wessex, which then imposed its system of shires, boroughs (or burhs) and ealdormen on Mercia after it came under West Saxon control during the 9th century".

Berkshire History for Kids (!) is more specific, if not entirely sure: "King Athelwulf of Wessex seems to have made Berkshire a county in the 840s."

Æthelwulf (as we should spell his name) was Alfred's father. So it seems that the answer is (probably) Yes: in King Alfred's day, Wantage was in Berkshire.