Re the New Steam Mill
That is part of the identification issue. There is a map of about the mid 1830's which shows it (in Birmingham Canal Navigations Society Archives) where it is next to the Honduras Wharf. This "New Steam Mill" seems to have been associated, at that time with the rolling of metals, but it did let of power to others, such as the timber wharf. In 1850 the trade directory mentions different tenants and later still it was the Eagle Flour Mill.
The Old Steam Mill was first on a plot of land near Water Street and is shown on a map of Birmingham prior to the making of the Birmingham & Fazeley Canal. It was here that James Pickard used a steam engine that was the first to adopt rotative motion. Pickard occupied property that extended from Water Street to Lionel Street and the canal bisected that property. The steam mill was developed as two separate functions, where the rolling of metals and the milling of flour was conducted. By the 1830's the Metal Rolling Mill had a separate identity to the flour mill, which by then, this flour mill was on the corner of Water Street and Snow Hill. Samuel Parker had the flour mill, then. The separate rolling mill was occupied by the Muntz family who had become known for the making of sheathing metal for ships. It was Rayner, a later occupant of the Old Steam Mill that transferred the mill to Snow Hill Wharf and the Muntz mill was finally occupied by Kynoch's until the GWR needed part of the mill site for their Snow Hill station expansion.
Parker and later Rayner had it seems little access to the canal as there was a Timber Yard, Muntz Mill and the Phoenix Foundry between the flour mill and the canal and it is possible that the Snow Hill Wharf warehouses were used to assist the Old Steam Mill trade until they moved their mill there. The mill is shown on the 1st Edition Ordnance Survey as being on Snow Hill Wharf, so the move would have been prior to this survey.