Downham Market If you're looking for property to rent in Downham Market, OpenArch have a variety of options. Over the past few decades, Downham Market has grown from a quiet market town to a thriving modern area with supermarkets, cafes and restaurants. The centre is full of historic buildings and the attractive market place has an unique black and white clock as its centrepiece. The town is well-equipped with facilities, offering both a modern leisure centre and a weekly market. Nearby larger towns include Kings Lynn and Wisbech.