There is some great footage of Millhouses Park (and other City parks) on this great archive footage on the BFI player. Shot in the 1960’s it shows how popular the park has always been with great scenes of the old paddling pools (now where the fish pass is) and also the old slide and geometric climbing frame.
you can watch it for free at (Millhouses Park is at 6:40 onwards)!
https://player.bfi.org.uk/free/film/watch-sheffield-parks-and-gardens-1964-online