Dark matter is the dominant form of matter in the Universe, but its nature is unknown. It is plausibly an elementary particle, perhaps the lightest supersymmetric partner of known particle species. In this case, annihilation of dark matter in the halo of the Milky Way should produce γ-rays at a level that may soon be observable. Previous work has argued that the annihilation signal will be dominated by emission from very small clumps (perhaps smaller even than the Earth), which would be most easily detected where they cluster together in the dark matter haloes of dwarf satellite galaxies. Here we report that such small-scale structure will, in fact, have a negligible impact on dark matter detectability. Rather, the dominant and probably most easily detectable signal will be produced by diffuse dark matter in the main halo of the Milky Way. If the main halo is strongly detected, then small dark matter clumps should also be visible, but may well contain no stars, thereby confirming a key prediction of the cold dark matter model.