(edited) Our article is now available online in Phys. Rev. Lett. !
In presence of impurities, ferromagnetic and ferroelectric domain walls slide only above a finite external field. Close to this depinning threshold, they proceed by large and abrupt jumps, called avalanches, while, at much smaller field, these interfaces creep by thermal activation. In this work we develop a novel numerical technique that captures the ultra-slow creep regime over huge time scales. We point out the existence of activated events that involve collective reorganizations similar to avalanches, but, at variance with them, display correlated spatio-temporal patterns that resemble the complex sequence of aftershocks observed after a large earthquake. Remarkably, we show that events assembly in independent clusters that display at large scales the same statistics as critical depinning avalanches. We foresee this correlated dynamics being experimentally accessible by magneto-optical imaging of ferromagnetic films.