Islanded multi-microgrids (MMGs) can provide reliable emergency power supply during extreme events. However, under complex operating conditions and disturbances, the effectiveness of this capability depends critically on the design of power supply strategies and the dynamic response performance of power system. To address this challenge, this paper proposes an emergency power supply strategy for MMGs based on improved finite-time consensus algorithm. The proposed strategy achieves frequency and voltage regulation, day-ahead preventive dispatch, and intra-day emergency control through consensus cooperation among agents. The day-ahead preventive dispatch comprises the optimization of distributed generator (DG) outputs at the microgrid (MG) level and power coordination at the MMG level, achieving inter-MG coordination while respecting the autonomy of individual MGs. In the presence of any disturbances, the intra-day emergency control adjusts DG outputs in real time according to their respective participation factors to maintain the scheduled power exchanges among MGs, thus enhancing the robustness of the proposed strategy. Furthermore, the improved finite-time consensus algorithm significantly accelerates the convergence speed of the solution. Case studies based on an MMG simulation model are conducted to verify the effectiveness and superiority of the proposed strategy.