There's a claim that Cromwell's Bridge was Tolkien's inspiration for the Shire's Brandywine Bridge in The Lord of the Rings; in addition the layout of the three converging rivers in the area - Hodder, Calder and
Ribble - is very similar to Tolkien's map of the Shire's rivers. Check it if you're a Tolkien fan.
It's certainly true that the bridge would've been present when Cromwell was marching the New Model Army to Preston to fight the Royalists, and it was on his route. It was built as a packhorse bridge around the 1560s, but I have heard from local historians that it was most probable it was only used by the luggage train carrying arms and other supplies that could not be risked in water; everything and everyone else had to go through the water. It would've taken far too long for everyone to cross the bridge which is very narrow, only an animal's width so maybe two people's width. Maybe Cromwell rode across it but maybe he didn't - being at the head of the luggage train wouldn't have been half as impressive, inspirational or encouraging as being at the head of his Army!
When I lived in a nearby village, the local children referred to it as the Fairy Bridge ...