No one seems to know how the name ‘Monkey Bridge’ came about.

Image: Doc Brown’s Travel Pictures
It’s actually the foot-bridge that crosses the railway line from what is now Kendricks Fold to the River Estate (Severn Road, Dee Road etc). Prior to the Kendricks Fold Estate being built, access to it from Warrington Road was via a footpath that ran along the side of Wood’s Foundry at the end of which was a field which led on to the bridge.
The footpath was a popular place for courting couples as at the bottom of the footpath, the wall of the foundry was warm as behind it was the foundry furnace!

Image: Brian Renshall
The most popular theory as to the name ‘Monkey Bridge’ is that the bridge was constructed of metal cross pieces which ran the full length over the railway line. These were perhaps thought to be similar to ‘Monkey Bars’ hence the name.
Sadly the bridge is not what it used to be having been altered to satisfy Health & Safety regulations.