Step Two: the brooks
Nudge. Each of the three lines rules something out. Start with the dyke: it only runs through one row of fields.
Harder
The dyke row is four fields. East of the mill and beyond the withies leaves two of them. The sluice keeper's meadow is the one with the gates in it.
The step, in words
The plan is a grid of twelve fields, four across and three down, with north at the top. Top row, west to east: Mill Brook, Tithe Mead, Rope Walk, Ferry Piece. Middle row: Church Field, Long Withies, Sallow Brook, Sluice Meadow; the dyke runs through all four of these, from the Knucker Hole at the west end to the sluice gates at the river on the east. Bottom row: Pound Mead, Cudlow Piece, Heron Marsh, Wharf Brooks. The mill stands in the north-west corner in Mill Brook, the church is west of Church Field, the river runs down the east side, and the castle is off the top of the map to the north. Every field is a button, named, in that arrangement. Tap one and then Go there.
The answer
Sallow Brook, the third field of the dyke row.
The dyke runs through the middle row: Church Field, Long Withies, Sallow Brook, Sluice Meadow. East of the mill and beyond the withies leaves Sallow Brook and Sluice Meadow. The sluice keeper has walked his meadow and seen nothing, so it is Sallow Brook. The Hole was never where it lived. It drinks there.