Understanding the processes underlying development and persistence of polarised opinions has been one of the key challenges in social networks for more than two decades. While plausible mechanisms have been suggested, they assume quite specialised interactions between individuals or groups that may only be relevant in particular contexts. We propose that a more broadly relevant explanation might be associated with the influence of external events. An agent-based bounded-confidence model has been used to demonstrate persistent polarisation of opinions within populations exposed to stochastic events (of positive and negative influence) even when all interactions between individuals are noisy and assimilative. Events can have a large impact on the distribution of opinions because their influence acts synchronistically across a large proportion of the population, whereas an individual can only interact with small numbers of other individuals at any particular time.