Was it a roman villa in winchester? Was there a roman villa in winchester?
I don't think the show even mentions that the king of wessex has his main residence at winchester, though.
Although the West Saxon capital was nominally at Winchester, Anglo-Saxon kingship was heavily itinerant, and royal power was spread through a vast array of local sites. Administration largely took place at the 'Hundred' and Shire levels, by the late ninth century centred around the network of 'burhs'. Before and contemporary to that series, a vast panoply of royal 'vils' and 'tuns' acted as centres of authority. Ecgbehrt was a Cerdicing, whose family church was at Wimborne Minster in Dorset. Alfred's brother Æthelred is still buried there today. The neighbouring site of Kingston Lacy was a royal 'tun', and indeed Edward the Elder marshalled an army there when his cousin Æthelbold tried to capture Wimborne in the 890s. The long and short of this is that Ecgberht's villa, if it existed, need not have been at Winchester at all.
Whether or not Ecgberht had a villa is, so far, unknown. I've written before on the importance of Romanitas in Anglo-Saxon political life, and having your own Romanesque house would certainly be a show of power. Ecgberht certainly did embrace propaganda opportunities - he mints a series of coins proclaiming his rule of London in 829 even though he holds the city less than a year - and so we might expect more to be made of his having restored a Roman villa.
Roman villa complexes in an agricultural setting tend to have vanished long before the 9th century, however, as changes in agriculture and land use render them obsolete. Excavations at Stafford for example show that the Roman villa complex on the site had completely collapsed and the area returned to wilderness centuries before the Burh was established on the site in 911. A surviving rural villa in sufficient condition to be repaired and inhabited by the 820s is quite unlikely. In an urban setting things are potentially somewhat different.