1. A method of data processing in a data processing system, the method comprising: at a cache memory of a data processing system, receiving a transactional memory access request generated by execution by a processor core of a transactional memory access instruction within a requesting memory transaction, wherein the transactional memory access request includes a target address of data to be accessed; in response to execution of a transactional memory instruction within the requesting memory transaction, said transactional memory instruction including a field that indicates a priority of the requesting memory transaction, the processor core indicating to the cache memory the priority of the requesting memory transaction; in response to the transactional memory access request, a transactional memory circuit in the cache memory detecting a conflict for the target address between the transactional memory access request and a transaction footprint of an existing memory transaction; the transactional memory circuit accessing a priority of the existing memory transaction; in response to detecting the conflict, the transactional memory circuit resolving the conflict by causing the cache memory to fail one of the requesting memory transaction and the existing memory transaction based at least in part on the relative priorities of the requesting memory transaction and the existing memory transaction, wherein resolving the conflict includes at least: causing the cache memory to fail the existing memory transaction when the requesting memory transaction has a higher priority than the existing memory transaction, the transactional memory access request is a transactional load request, and the target address is within a store footprint of the existing memory transaction; and the transactional memory circuit increasing a priority of a memory access within the existing memory transaction in response to receipt from the processor core of an indication of a priority of a nested memory transaction enclosed within the existing memory transaction.