The (re)ionisation of hydrogen in the early universe has a profound effect on the formation of the first galaxies: by raising the gas temperature and pressure, it prevents gas from cooling into small haloes thus affecting the abundance of present-day small galaxies. Using the Galform semi-analytic model of galaxy formation, we show that two key aspects of the reionisation process -- when reionisation takes place and the characteristic scale below which it suppresses galaxy formation -- are imprinted in the luminosity function of dwarf galaxies. We focus on the luminosity function of satellites of galaxies like the Milky Way and the LMC, which is easier to measure than the luminosity function of the dwarf population as a whole. Our results show that the details of these two characteristic properties of reionisation determine the shape of the luminosity distribution of satellites in a unique way, and is largely independent of the other details of the galaxy formation model. Our models generically predict a bimodality in the distribution of satellites as a function of luminosity: a population of faint satellites and population of bright satellites separated by a valley forged by reionisation. We show that this bimodal distribution is present at high statistical significance in the combined satellite luminosity function of the Milky Way and M31. We make predictions for the expected number of satellites around LMC-mass dwarfs where the bimodality may also be measurable in future observational programmes. Our preferred model predicts a total of $26 pm 10$ (68 per cent confidence) satellites brighter than ${rm M}_V=0$ in LMC-mass systems.
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