ABSTRACT Recent anisotropy studies of UHECR data at energies ≳40 EeV have disclosed a correlation of their angular distribution with the extragalactic local structure, specifically with either local starburst galaxies or AGN. Using Monte Carlo simulations taking into account photodisintegration processes, we further explore a framework in which these UHECRs were accelerated by Centaurus A in a recent powerful outburst before being scattered by magnetic fields associated with local, Council of Giant, extragalactic structure. We find that the observed intermediate-scale anisotropies can be accounted for by the Council of Giant structure imposing a response function on the initial outburst of UHECRs from a single source located at Centaurus A’s position. The presence of these local structures create ‘echoes’ of UHECRs after the initial impulse and focusing effects. The strongest echo wave has a lag of ∼20 Myr, comparable to the age of synchrotron-emitting electrons in the giant Centaurus A lobes. Through consideration of the composition of both the direct and echo wave components, we find that the distribution of the light (1 < ln A < 1.5) component across the sky offers exciting prospects for testing the echo model using future facilities such as Auger prime. Our results demonstrate the potential that UHECR nuclei offer, as ‘composition clocks’, for probing propagation scenarios from local sources.