OpenStreetMap now largely matches https://waterwaymap.org/#map=14.67/52.92294/-1.47443&len=10..inf&tiles=planet-waterway-water https://www.openstreetmap.org/way/1256155771 https://www.openstreetmap.org/way/1267369302

As well as Sadlergate Bridge https://www.openstreetmap.org/way/27014613 the brook goes under Saint James’ Bridge https://www.openstreetmap.org/node/11771064345 Saint Peter’s Bridge https://www.openstreetmap.org/node/11771064351 and Tennant (Street) Bridge https://www.openstreetmap.org/node/11773245451 https://her.derbyshire.gov.uk/Monument/MDR11504 none of which are visible from above ground today

Outflow of Markeaton Brook to the Derwent in the Riverside Gardens has been blocked off with the flow diverted to Mill Fleam https://www.openstreetmap.org/way/29291874

Need further research to find the route near here https://www.openstreetmap.org/way/179863424 to trace other underground flows https://www.openstreetmap.org/note/4174133 and to further improve the alignment
