Teignmouth is a seaside town, fishing port and civil parish in the English county of Devon. It is on the north bank of the estuary mouth of the R…Teignmouth is a seaside town, fishing port and civil parish in the English county of Devon. It is on the north bank of the estuary mouth of the River Teign, about 12 miles south of Exeter. The town had a population of 14,749 at the 2011 census.