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, and wherein the memory move instruction sequence includes an explicit instruction identifying a beginning of the memory move instruction sequence and an explicit instruction identifying an ending of the memory move instruction sequence; in response to receipt at the lower level cache 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; in response to receipt at the lower level cache 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; in response to receipt at the lower level cache from the processor core of a request corresponding to the explicit instruction identifying the ending the memory move instruction sequence, the lower level cache providing an indication to the processor core of whether an entire memory move specified by the memory move instruction sequence completed successfully or not; and the processor core, in response to the indication, updating one or more state flags in the processor core tracking success or failure of the memory move.