An apparatus and method are provided for making predictions for instruction flow changing instructions. The apparatus has a fetch queue that identifies a sequence of instructions to be fetched for execution by execution circuitry, and prediction circuitry for making predictions in respect of instruction flow changing instructions, and for controlling which instructions are identified in the fetch queue in dependence on the predictions. The prediction circuitry is arranged, during each prediction iteration, to make a prediction for a predict block comprising a sequence of M instruction addresses, in order to identify whether that predict block contains the instruction address for an instruction flow changing instruction that is predicted as taken. During each prediction iteration, the prediction circuitry is arranged by default to access a prediction storage in order to produce prediction information for instructions associated with a specified block of instruction addresses (including at least the predict block being considered), and to use that prediction information to make the prediction for the predict block. Buffer storage is used to retain the prediction information obtained from the prediction storage during one or more previous prediction iterations, and detection circuitry is used to detect when a current predict block being considered during a current prediction iteration comprises one or more instruction addresses for which the associated prediction information is retained in the buffer storage. In that event, the above default behaviour is not adopted, and an override condition is triggered to cause the prediction information for those one or more instruction addresses to be obtained from the buffer storage rather than from the prediction storage, giving rise to a power saving.