Whole body model predictive control (WBMPC) is a powerful tool to generate complex robotics motion. Despite the recent increase in computational capabilities with new processors such as the Apple chipsets (M1, .. M3) or GPUs, WBMPC algorithms need a significant amount of computational time. This induces delay, which, if not properly accounted for, can have detrimental effects on the controller's performance. This paper conducts a detailed study to understand the impact of delay on WBMPC and proposes an efficient solution to handle it effectively. In this regard, a whole-body control task is formulated as an optimal control problem and solved using the Differential Dynamic Programming (DDP) solver. An extensive amount of numerical studies are carried out to understand the nature of the problem and thereby devise an effective solution. The proposed solution is found to be effective numerically, and it has been experimentally verified with the humanoid TALOS. Both numerical and experimental results are presented and discussed in this work to provide valuable incites.