The museum was established as the Design Collection in 1988 and awarded registered museum status by the Museums, Libraries and Archives Council in 2001. It changed its name to the Museum of Design in Plastics on 1 September 2007 to reflect the decision to focus on plastics and became the UK's only fully accredited plastics museum in September 2008. In 2022 its collection was awarded Arts Council England's 'Designated status' in recognition of its national and international importance.

MoDiP is now acknowledged as the UK's leading resource for the study and interpretation of design in plastics. As such it is a major research resource, supporting academic study and research across the HE/FE sectors as well as providing a resource for professional curators throughout the UK and internationally.