I'm an archaeologist who used to live on the same road as the Hall. Prenton is quite an interesting area, as it is one of only a handful of Wirral mill sites mentioned in Domesday (another being at Bromborough). The mill site is known, and it's likely that the Hockenhull family owned the lands it was situated on. Prenton was also home to forested area in Domesday. This is not necessarily a forest as you would think now, but was an area of land that was not allowed to be fenced or restricted to allow game such as deer and boar to roam.
The estate was owned by Walter de Vernon at Domesday, who was one of William I's chums. Always wanted to undertake a geophysical survey at Prenton Farm Hall. I suspect that there will be evidence of a much earlier building within the grounds.