Using the data set of the three hundred project, i.e. a suite of 324 hydrodynamical resimulations of cluster-sized haloes, we study galaxy cluster mergers and their effect on colour and luminosity changes of their brightest cluster galaxies (BCG). We track the main progenitor of each halo at z = 0 and search for merger situations based on its mass accretion history, defining mergers as very rapid increases in the halo mass. Based upon the evolution of the dynamical state of the cluster we define a pre-and post-merger phase. We create a list of all these events and statistically study their mass ratio and time-scales, with the former verifying that all instances are in fact major mergers. By comparing to a control sample of clusters without mergers, we study the effect mergers have on the stellar component of the BCG. Analysing the mass, age, and metallicity of the BCG stellar particles, we find that the stellar content of BCGs grows significantly during mergers and, even though the main growth mechanism is the accretion of older stars, there is even a burst in star formation induced by the merger. In our simulations, BCGs in mergers form in median around 70 per cent more stars than those normally growing, although this depends on the radius considered for defining the BCG. Regarding observable properties, we see an increase in SDSS-u luminosity of 20 per cent during mergers, accompanied by a slightly slower increase of the galaxy g-r colour as compared to the control sample.