Next to the where the Friar Penketh pub has been built, directly opposite the old theatre there used to be a tiny pub. In that pub there were steps leading down to what you first might expect to be a cellar but was in fact the entrance to a tunnel. The tunnel was about 5ft high, 3ft wide with old wooden supports and about 6-8ft in was blocked off with planks of modern type wood, you could see through gaps in the planks that the tunnel went further. I saw it in the 70's.
I don't find it difficult to believe that there could have been tunnels under the town at some stage, but I don't think that they would have been dug by Cromwell's men - when would they have had the time? and why would they dig them? They came here to fight not hide.
Rumour has it, that there was a tunnel from the academy to the parish church. I think any tunnels would far predate these. I think it's more likely that there were tunnels from the friary and from the parish church site - where there has been some kind of a church since circa 650 - both leading to the old Motte castle. So, by using these tunnels one could get from the friary to the church. These could have been the routes to safety for the religious orders if ever the town was attacked. The old Motte castle would have been where everyone in the town would have fled to safety.
As for construction, I doubt they were 'hewn from rock'. They could have been made simply by digging trenches. putting the framework in and filling in above with a foot or two of soil. The purpose of these tunnels would merely have been to get them, unseen and protected to the castle. There were probably other tunnels from the friary surfacing in different locations around the town, giving them alternative escape routes should the friary be raided. The religious orders would be obvious targets for raids, having valuable icons etc and during the persecutions, considering the brutal deaths they would suffer if caught, it would seem to me stupid of them not to have devised some form of escape routes.