Grampus Heritage is leading the community excavation on land owned by Robert and Edmund Jackson.
Archaeologists found evidence of walls of a large Roman building, shards of pottery and metal objects.
The excavation is part of a development phase before the non-profit organisation puts in a full application bid in March for £200,000 to the Heritage Lottery to fund a three-year project.
The team hopes the project will build a picture of the Roman heritage along the banks of the River Derwent at Cockermouth and Papcastle.
Phase one of the bid has already been accepted, providing funding for six months and the cash was used for the two-week dig and a further six days of digging at an unconfirmed location, which will show the team where resources should be directed for the main project.
Archaeologist Mark Graham said: “It is too early to identify exactly what the building was used for but we have to ask ourselves was this a Roman bath house or could it have been used as a high status building for an official person in the town? Read more.