My 3 favorites are:
Baddesley Clinton a moated manor house near Warwick that was built in the late 13th century
Lower Brockhampton another moated manor house, it is near Bromyard and also dates from the late 14th century.
And Stokesay Castle (it's not, it has crenalation but it's a manor house not a castle) is 13th century and is located near Craven Arms. It's not moated but wonderful anyway,
I've been looking at estate agent pictures from England and I've decided that if we ever win the lottery we're going to but a manor house!