Context. A collisional avalanche is set off by the breakup of a large planetesimal, releasing vast amounts of small unbound grains that enter a debris disc located further away from the star, triggering there a collisional chain reaction that could potentially create detectable transient structures. Aims. We investigate this mechanism, using for the first time a fully self-consistent code coupling dynamical and collisional evolutions. We also quantify for the first time the photometric evolution of the system and investigate whether or not avalanches could explain the short-term luminosity variations recently observed in some extremely bright debris discs. Methods. We use the state-of-the-art LIDT-DD code. We consider an avalanche-favoring A6V star, and two set-ups: a “cold disc” case, with a dust release at 10 au and an outer disc extending from 50 to 120 au, and a “warm disc” case with the release at 1 au and a 5−12 au outer disc. We explore, in addition, two key parameters: the density (parameterized by its optical depth τ) of the main outer disc and the amount of dust released by the initial breakup. Results. We find that avalanches could leave detectable structures on resolved images, for both “cold” and “warm” disc cases, in discs with τ of a few 10-3, provided that large dust masses (≳1020−5 × 1022 g) are initially released. The integrated photometric excess due to an avalanche is relatively limited, less than 10% for these released dust masses, peaking in the λ ~ 10−20 μm domain and becoming insignificant beyond ~40–50 μm. Contrary to earlier studies, we do not obtain stronger avalanches when increasing τ to higher values. Likewise, we do not observe a significant luminosity deficit, as compared to the pre-avalanche level, after the passage of the avalanche. These two results concur to make avalanches an unlikely explanation for the sharp luminosity drops observed in some extremely bright debris discs. The ideal configuration for observing an avalanche would be a two-belt structure, with an inner belt (at ~1 or ~10 au for the “warm” and “cold” disc cases, respectively) of fractional luminosity f ≳ 10-4 where breakups of massive planetesimals occur, and a more massive outer belt, with τ of a few 10-3, into which the avalanche chain reaction develops and propagates.