Okay, with Ojay's help I think we've pretty much uncovered this.
I was wrong in that the bridge in the background of the photograph is not the currently extant bridge - those who've seen Optimus Prime threads will no doubt have seen the bricked up arches at the same level, just a bit further down: it seems that that is the location of the 'second' bridge. So, we actually have a photo of the bridge that is no longer there.
What this does reveal is that the 'cattle bridge' dates back no further than, at a rough guess, the 1860s, maybe a little after: it is a replacement of the original bridge seen in my photo to be crossing the Irk just above water level. Other than Ojay's photo of Walkers Croft showing the location of the bridge with respect to Todd Street, what led me to this conclusion was this extract from Tom Wray's book on Victoria:
'The squalid approach to the station from Todd Street by way of Mill Brow remained a bone of contention for many years. A letter of the 2 November 1853 describes the situation succinctly, Mill Brow ".... is exceedingly inconvenient and annoying especially in wet weather .... should you be going to the station, you descend the brow as gently as possible, arrive at the wooden bridge, and are preparing to ascend the incline plane before you, when, ten to one, down rushes a multitude, which an arrival train has just disgorged, and which, like a flood, carries all before it .... I do with all due respect (suggest) a viaduct might be built from the station to Todd Street, both being nearly on the same level".'
Check that out! The suggestion of a new bridge attaining to the level of Todd Street rather than having to put the poor denizens of Manchester through trudging down the slippery cobblestones of Mill Brow.
So there we have it. The 'cattle bridge' was a replacement footbridge, built by the Lancashire & Yorkshire Railway to replace the earlier one, which may well have been very old indeed, and led, probably, up to Todd Street. At a guess, the 'second' bridge we only have the bricked up archways of probably just led to the graveyard from Corporation Street.
I will be forever in the favour of the person who can find a photograph of the 'cattle bridge' before it was covered over, since throughout this we have lost that!