1. A method of data processing in a data processing system including a processor core having a store-through upper level cache and a store-in lower level cache, the method comprising: in response to execution by the processor core of a memory move instruction sequence including a plurality of copy-type instructions and a plurality of paste-type instructions, the processor core transmitting a corresponding plurality of copy-type and paste-type requests to the lower level cache, wherein each copy-type request specifies a source real address and each paste-type request specifies a destination real address; in response to receipt of each copy-type request, the lower level cache copying a respective one of a plurality of data granules from a respective storage location specified by the source real address of that copy-type request into a non-architected buffer; and in response to receipt of each paste-type request, the lower level cache writing a respective one of the plurality of data granules from the non-architected buffer to a respective storage location specified by the destination real address of that paste-type request.