Swinton is a town in the Metropolitan Borough of Rotherham, in South Yorkshire, England on the west bank of the River Don. It has a popul…Swinton is a town in the Metropolitan Borough of Rotherham, in South Yorkshire, England on the west bank of the River Don. It has a population of 15,559. The town is five miles north-northeast of the larger town of Rotherham and south-west of Mexborough. The original junior and infant school building built in 1852 on Church Street still exists, and is being converted into residential apartments called Fitzwilliam Lodge.