You may need to supply more details. To my knowledge there has never been a mill by the Greenses. The nearest mill that would have been known by your grandfather would probably have been Tommy the Miller’s mill (the Castle Mill) at the top of Coronation Park (see Park Life pt2). However the area south of Lords Mount did have various windmills in the 16th century and maybe much later.
There was, until the 1990’s (?) the small Vulcan Foundry in the Greenses that might be described as a steel mill. That seems unlikely but it may be the factory you refer to. As you can see from the maps, a large ropery existed behind the walls. This is Berwick’s earliest ropeworks started by George Loch in the 18th century. Apart from that there is little industry in this residential area.
John Wood’s 1822 map of Berwick shows how undeveloped the Greenses area was at that time. The situation is not much improved by 1852. The open fields of this area since the mediaeval period gives the area its name.
It seems hard to imagine today but Lords Mount was filled in until excavated in the 1970s. This gun tower from the early 1540s, said to be designed by Henry VIII has six gun ports. These were known locally as “the Devil’s ovens” from their outward appearance. This was built on the site of a mediaeval bell tower, part of the early 14th century walls. (The Bell Tower we know today was built in 1577.)
To my knowledge, very few Roman remains have been found in the Berwick area (see earlier answer) and none in this area. What your grandfather may have been thinking of was the find of a stone “sarcophagus” in 1911 when the houses on Northumberland Avenue were being built. There was an exchange of opinion in letters in an Edinburgh paper at the time as to whether it was for Edward I as it was some 7 ft long and had the inscription “E I” inside. This is unlikely as Edward died in Grange-over-Sands in Cumbria and wouldn’t have styled himself “E I” – that is a much later notion (not that the first monarch with any name adds “I”). It was taken to the back yard of the museum of the time (which would have been at the side of Jim Youngmans carpet shop between Crawford’s Alley and Chapel Street. It is noted in an inventory of 1926 but its whereabouts are now unknown.