The Newcastle Libraries Photograph Collections has the two old photographs shown below including one from 1968, just before the tower was demolished (click the photos for the links).
There is a good summary of the history of the lead industry here on the Newcastle University website, Structural Images of the North East (SINE).
By 1779, their Elswick works was producing white lead, and by the mid-1780s the concern was generating some £3,000 annual profit and a 30 per cent increase in turnover, while diversifying into red lead, lead rolling and, from 1797, into lead shot. The Elswick shot tower was one of the earliest to be built, being in operation by 1797. At 174 feet high and with a drop of 150 feet it was a notable feature of the area. In 1825 Mackenzie described it as a:
… most striking and remarkable object…It is a circular brick building, with a stone cupola, terminated by a chimney, and is ascended by a winding staircase in the interior. This singular edifice presents itself to travellers about two miles north of Chester le Street and never fails to exite their curiosity.
Mackenzie also repeated a story to the effect that shortly after its completion the tower was found to be ‘alarmingly out of perpendicular' but that this was corrected by the simple expedient of digging away the earth from its more elevated side until it recovered its perpendicularity. Thus Tyneside lost its ‘Leaning Tower of Elswick'. Shot production ceased in 1951 and although the tower was soon after listed as an Historic Building, it appeared to go back to its old habit of leaning and had to be demolished in 1968/69
The same source has this rather more romanticised view published in the Beauties of England and Wales in 1806.
Droplets are formed by forcing a molten alloy of lead, antimony and arsenic through holes in a sieve at the top of the tower. After the fall, the shot is caught and cooled by falling into a deep basin of cold water at the base. After Watt's patent, which was a huge improvement on shot previously made by casting, there was little further change apart from adding an updraught of air, and ways to sort out deformed shot.
Watts's old house in Bristol - his original shot tower - kept producing shot until 1968. The full story can be read here.
In an interesting connection with Heddon, the latter author reports that slag from the blast furnace at Elswick Lead Works was eventually recycled – to reinforce the Tyne riverbank on the north side between Newburn and the Hedwin streams.
To me, there’s a certain sadness that the place is no more. It was a Newcastle institution in its heyday, and a great many very fine people worked there.
Coop's Tower in Melbourne has been preserved under a 84m high conical glass roof of a shopping centre.
Many more, like those at Elswick, and at Lambeth on London's South Bank (above right), were demolished when their productive use was no longer necessary.