Correlations between intrinsic ellipticities of galaxies are a potentially important systematic error when constraining dark energy properties from weak gravitational lensing (cosmic shear) surveys. In the absence of perfectly known galaxy redshifts, some modelling of the galaxy intrinsic alignments is likely to be required to extract the lensing signal to sufficient accuracy. We present a new model based on the placement of galaxies into dark matter haloes. The central galaxy ellipticity follows the large-scale potential and, in the simplest case, the satellite galaxies point at the halo centre. The two-halo term is then dominated by the linear-alignment model and the one-halo term provides a motivated extension of intrinsic alignment models to small scales. We provide fitting formulae for the spatial projected source power spectra for both intrinsic–intrinsic (II) and gravitational–intrinsic (GI) correlations. We illustrate the potential impact of ignoring intrinsic alignments on cosmological parameter constraints from non-tomographic surveys, finding that σ8 could be underestimated by up to the size of the current 1σ error bar from cosmic shear if very small scales are included in the analysis. Finally, we highlight areas of interest for numerical simulations of dark matter clustering and galaxy formation that can further constrain the intrinsic alignment signal.