1. A method of data processing in a data processing system, the method comprising: a processor core generating a store operation by executing a store instruction in an instruction sequence; selectively marking the store operation as a high priority store operation, wherein the selectively marking includes: marking the store operation as a high priority store operation in response to detecting a barrier instruction in the instruction sequence immediately preceding the store instruction in program order; and refraining from marking the store operation as a high priority store operation in response to not detecting a barrier instruction in the instruction sequence immediately preceding the store instruction in program order; buffering the store operation within a store queue associated with a cache memory of the processor core; and expediting handling of the store operation in the store queue in response to the store operation being marked as a high priority store operation and otherwise refraining from expediting handling of the store operation in the store queue.