Leicester is west of Worcester and includes a mix of village-center homes, some well over a century old, and newer houses on the outskirts. The older ones often have stone foundations laid without any waterproofing at all, built at a time when a damp cellar was simply expected.
You can't make an old stone wall watertight, but you can control where the water goes. The usual approach is an interior drain along the base of the wall feeding a sump pump, with a plastic membrane on the wall that directs seepage down into the drain and keeps the space drier. Adding a dehumidifier afterward helps with the musty smell. If you're planning to finish an old basement, get the water under control first; it's much harder to fix after the walls are framed. Ask the company whether its warranty covers the whole system or only parts of it.