They must have got pretty tired of it, though, because apprentice cutlers had a clause written into their contracts stipulating the poor souls wouldn’t have to eat salmon more than three times a week.
The stretch of riverbank used for catching the fish was known as Salmon Pastures, but come the Industrial Revolution the name sounded like a music hall joke.
Once-verdant meadows were replaced by a hideous coke works surrounded by slag heaps.
As for the river, George Orwell travelled through Sheffield in the 1930s while writing The Road to Wigan Pier and described its water as “usually bright yellow with some chemical or other.”
By then, of course, the salmon, trout and eels which once fed local people were long departed and the Don was one of Europe’s most poisoned rivers.
So I was thrilled to see the £300,000 Hadfield Weir fish and eel pass last week while visiting Meadowhall shopping centre.
Never mind that no salmon are yet to be seen leaping majestically upstream to spawn, although someone on social media joked about spotting an empty tin of salmon carried along by the current.
The exciting thing about the fish pass is that the Don is considered ready to attract salmon back to its upper reaches for the first time since the Middle Ages.
The water quality is certainly now capable of supporting fish, although you are unlikely to hear Ukip candidates making this point.
That’s because the remarkable clean-up of the Don and other once heavily polluted Yorkshire rivers like the Aire and Calder is due to something called the EU Water Framework Directive (2000) passed in Brussels and implemented in the UK three years later, which set out stringent targets for the Environment Agency to achieve through ever-tightening controls on discharges from sewage works and industry.
Species of wildlife considered bellwethers of a river’s health - otters, dippers, kingfishers, brown trout - have become re-established, and the Don’s full rehabilitation is years rather than decades away.
The first salmon for two centuries was found downstream at Doncaster in 1995, and now only the physical barriers of weirs and damns which harnessed water power to drive industrial wheels stand in the way of the ultimate goal of bringing Atlantic salmon back to the spawning gravels of the upper Don and tributaries like the Dearne and Rother.
Another step towards that objective was taken in February with the opening of a £500,000 fish and eel pass at Sprotbrough.
A further nine weirs between there and Sheffield still require adapting for fish, but slowly the work is being done.
One day Salmon Pastures, which has been cleaned of its coke works and slag heaps and transformed into a nature reserve run by the Sheffield Wildlife Trust, will once again be worthy of the name.