It is hoped that x-ray phase contrast imaging (XPCi) will provide a generational improvement in the effectiveness of mammography. XPCi is sensitive to the refraction which x-rays undergo as a result of the variation in x-ray propagation speeds within an object. XPCi is, however, seldom used in clinical applications owing mainly to a lack of suitable systems. The radiation physics group at UCL has previously designed and built an XPCi system sensitive to phase gradients in one dimension for application in security inspection. We present here the design methodology and final design of a prototype XPCi system sensitive to phase gradients in two directions for use in mammography. The technique makes efficient use of the flux available from a laboratory x-ray source, thus making it suitable for clinical use.