Sainsburys lays the blame for the problem on the alleged failure of WSP to use reasonable care, skill and diligence in designing the foundations.
J Sainsbury and Sainsburys Supermarkets are suing WSP for unspecified damages for breach of agreement.
The writ states that WSP agreed to act as civil and structural engineer for the project to build the superstore in December 1996 but breached the agreement.
Sainsburys was unavailable for comment and WSP refused to comment.
WSP will be responsible for the building design, including civil and structural, geotechnical and fire engineering services.
Total construction costs are estimated to be £140m with completion in autumn 2005. The tower will be mixed-use, made up of a hotel with residential units above, including penthouse suites.