Its exact position remains unconfirmed, which is itself a small puzzle: the mill was significant enough to appear in civic records stretching back centuries, to be depicted on one of the most important early maps of Dublin, and to lend its name to a lane that survived long enough to appear on John Rocque's 1756 map of the city. The name offers its own curiosity. The Urban Survey of Dublin City records it as deriving from the Irish Muilenn an cháca, meaning, with no diplomatic softening, the mill of the shit. The same survey suggests it may be identifiable with a mill near a bridge granted by a figure named Gillamurra to Christ Church Cathedral before the Norman arrival in Ireland.

The mill was one of three watermills belonging to the Hospital of Saint John the Baptist, a religious house that stood outside the city walls to the south-west of Ormonds Gate. The mills were powered by a watercourse drawn from the Odder river, and the arrangement was formally regulated by the city authorities. In 1457 the Dublin Assembly Roll recorded the granting of the water course to Saint John's House, and a year later the Dublin White Book set out a forty-year lease between the Mayor of Dublin and the Prior and brethren of the hospital. The lease permitted the Prior to construct a fosse, a drainage channel or ditch, running from the mill near the hospital cemetery to the city ditch, with the water then flowing freely to the Liffey. The Mayor and commonalty retained the right to supervise the water, to use it for washing, and, in time of need, to divert it to fill the city ditch. Annual rent was forty shillings of silver. After the Dissolution of the Monasteries in the late 1530s, the church of Saint John's was dismantled and its materials sold off under William Brabazon, under-treasurer of Ireland, while the three watermills were specifically excluded from the general grant of the site to Edmund Redman in September 1539, suggesting they retained practical value.

John Speed's 1610 map of Dublin is perhaps the most useful guide to what the landscape once looked like. It shows a watercourse running east to west along Saint Thomas Street, turning northward where it powered several mills shown opposite John's House, before the water continued toward the Liffey, probably entering it somewhere near the area now occupied by Watergate House on Usher's Quay. Archaeological work in 1997, carried out by Linzi Simpson beneath the north-east corner of the National College of Art and Design on Oliver Bond Street, uncovered a section of this watercourse. A separate assessment at the junction of Oliver Bond Street and Augustine Street identified a fifteenth-century watercourse known as the Glib Water, along with a red-brick culvert and slight timber remains that may be the last traces of revetments lining the original channel. These fragments, buried under a working art college and a junction of unremarkable Dublin streets, are all that is currently visible of what was once a functioning industrial waterway serving the medieval city.