A data processing system includes an execution pipeline that includes one or more programmable execution stages which execute execution threads to execute instructions to perform data processing operations. Instructions to be executed by a group of execution threads are first fetched into an instruction cache and then read from the instruction cache for execution by the thread group. When an instruction to be executed by a thread group is present in a cache line in the instruction cache, or is to be fetched into an allocated cache line in the instruction cache, a pointer to the location of the instruction in the instruction cache is stored for the thread group. This stored pointer is then used to retrieve the instruction for execution by the thread group from the instruction cache.