We investigate the outcome of Lotka-Volterra dynamics of ecological communities with random interaction coefficients and non-linear functional response. We show in simulations that the saturation of Holling type-II response stabilises the dynamics. This is confirmed in an analytical generating-functional approach to Lotka-Volterra equations with piecewise linear saturating response. For such systems we are able to derive self-consistent relations governing the stable fixed-point phase, and to carry out a linear stability analysis to predict the onset of unstable behaviour. We investigate in detail the combined effects of the mean and variance of the random interaction coefficients, the cut-off parameter of the non-linear response, and a symmetry parameter. We find that stability and diversity increases with the introduction of functional response, where decreasing the functional response parameter has a similar effect to decreasing the symmetry parameter. We also find biomass and diversity to be less dependent on the symmetry of interactions with functional response, and co-operation to no longer have a detrimental effect on stability. *