Conkwell is a hamlet in Winsley parish, Wiltshire, England, near the county border with North East Somerset. It is about 2.3 miles west of Bradford-on-Avon and 3 miles southeast of the city of Bath. The settlement was established to house the workers in the local stone quarries. The southern side is in Winsley, but the northern is in the Somerset parish of Bathf…Conkwell is a hamlet in Winsley parish, Wiltshire, England, near the county border with North East Somerset. It is about 2.3 miles west of Bradford-on-Avon and 3 miles southeast of the city of Bath. The settlement was established to house the workers in the local stone quarries. The southern side is in Winsley, but the northern is in the Somerset parish of Bathford.