Gressenhall Carre Mill was working in the 1300s.

In 1402 the Court Leet of Gressenhall fined a tenant 4d as a punishment for the making of a ditch at North Carre, barring the tenants of Gressenhall from coming above the water at Carre Mill.
The History of Gressenhall Mill and Mill House - Eric Puddy, 1966

As to the site of "Carre Mill at the north Carr", there is mention of the sluice and "mill gate" and "Winckles' Brook" (known as "Inglish Brook" in later records), this being the little stream which runs from north of the parish church towards the south of Gressenhall Green where it flows under a small bridge before joining the Scarning river to the east.
There are two patches of water on this stretch. One the "lake", is modern, and was dug out as a duck decoy, the other is a small rectangular area a few hundred yards further down stream, and I am of the opinion that the second manorial mill, later known as Carre Mill, was here, and that this originally formed part of the Carre mill pond. The old manor house stood northwest of the church before 1600 A. D. and the site would fit in with this assumption.
The History of Gressenhall Mill and Mill House - Eric Puddy, 1966

1402: Mill tenant fined 4d for making an unauthorised ditch