Future total-power single-dish H I intensity mapping (HI IM) surveys have the potential to provide unprecedented insight into late time (zz < 1) cosmology that are competitive with Stage IV dark energy surveys. However, redshifts between 0 < zz < 0.2 lie within the transmission bands of global navigation satellite services (GNSS), and even at higher redshifts out-of-band leakage from GNSS satellites may be problematic. We estimate the impact of GNSS satellites on future single-dish HI IM surveys using realistic estimates of both the total power and spectral structure of GNSS signals convolved with a model SKA beam. Using a model of the SKA phase one array with 200 dishes we simulate a HI IM survey covering 30 000 deg2 of sky. We compare the integrated GNSS emission on the sky with the expected H I signal. It is found that for frequencies >950 MHz the emission from GNSS satellites will exceed the expected H I signal for all angular scales to which the SKA is sensitive when operating in single-dish mode.