  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.
