We examine the extent to which the self-annihilation of supersymmetric neutralino dark matter, as well as light dark matter, influences the rate of heating, ionisation and Lyman-α pumping of interstellar hydrogen and helium and the extent to which this is manifested in the 21 cm global background signal. We fully consider the enhancements to the annihilation rate from DM halos and substructures within them. We find that the influence of such structures can result in significant changes in the differential brightness temperature, δT b . The changes at redsfhits z < 25 are likely to be undetectable due to the presence of the astrophysical signal; however, in the most favourable cases, deviations in δT b , relative to its value in the absence of self-annihilating DM, of up to ≃ 20 mK at z = 30 can occur. Thus we conclude that, in order to exclude these models, experiments measuring the global 21 cm signal, such as EDGES and CORE, will need to reduce the systematics at 50 MHz to below 20 mK.PACS numbers: 95.35+d