We have mesured the carrier recombination dynamics in InGaN/GaN multiple quantum wells over an unprecedented range in intensity. We find that at times shorter than 30,ns, they follow an exponential form, and a power law at times longer than 1,$mu$s. To explain these biphasic dynamics, we propose a simple three-level model where a charge-separated state interplays with the radiative state through charge transfer following a tunneling mechanism. We show how the distribution of distances in charge-separated states controls the dynamics at long time. Our results imply that charge recombination happens on nearly-isolated clusters of localization centers.