We investigate the production of electrons and positrons in the Milky Way within the context of dark matter annihilation. Upper limits on the relevant cross-section are obtained by combining observational data at different wavelengths (from Haslam, WMAP and Fermi all-sky intensity maps) with recent measurements of the electron and positron spectra in the solar neighbourhood by PAMELA, Fermi and HESS. We consider synchrotron emission in the radio and microwave bands, as well as inverse Compton scattering and final-state radiation at gamma-ray energies. According to our results, the dark matter annihilation cross-section into electron-positron pairs should not be higher than the canonical value for a thermal relic if the mass of the dark matter candidate is smaller than a few GeV. In addition, we also derive a stringent upper limit on the inner logarithmic slope α of the density profile of the Milky Way dark matter halo (α < 1 if m dm < 5 GeV, α < 1.3 if m dm < 100 GeV and α < 1.5 if m dm < 2 TeV) assuming that σv e± =3 × 10-26 cm3 s−1. A logarithmic slope steeper than α ∼ 1.5 is hardly compatible with a thermal relic lighter than ∼1 TeV, regardless of the dominant annihilation channel.