Network ecology holds great promise as an approach to modelling and predicting the effects of agricultural management on ecosystem service provision, as it bridges the gap between community and ecosystem ecology. Unfortunately, trophic interactions between most species in agricultural farmland are not well characterised empirically, and only partial food webs are available for a few systems. Large agricultural datasets of the nodes (i.e., species) in the webs are now available, and if these can be enriched with information on the links between them then the current shortage of network data can potentially be overcome. We demonstrate that a logic-based machine learning method can be used to automatically assign interactions between nodes, thereby generating plausible and testable food webs from ecological census data. Many of the learned trophic links were corroborated by the literature: in particular, links ascribed with high probability by machine learning corresponded with those having multiple references in the literature. In some cases, previously unobserved but high probability links were suggested and subsequently confirmed by other research groups. We evaluate these food webs using a new cross-validation method and present new results on automatic corroboration of a large, complex food web. The simulated frequencies of trophic links were also correlated with the total number of literature 'hits' for these links from the automatic corroboration. Finally, we also show that a network constructed by learning trophic links between functional groups is at least as accurate as the species-based trophic network.