Neuroimaging studies of the psychedelic state offer a unique window onto the neural basis of conscious perception and selfhood. Despite well understood pharmacological mechanisms of action, the large-scale changes in neural dynamics induced by psychedelic compounds remain poorly understood. Using source-localised, steady-state MEG recordings, we describe changes in functional connectivity following the controlled administration of LSD, psilocybin and low-dose ketamine, as well as, for comparison, the (non-psychedelic) anticonvulsant drug tiagabine. We compare both undirected and directed measures of functional connectivity between placebo and drug conditions. We observe a general decrease in directed functional connectivity for all three psychedelics, as measured by Granger causality, throughout the brain. These data support the view that the psychedelic state involves a breakdown in patterns of functional organisation or information flow in the brain. In the case of LSD, the decrease in directed functional connectivity is coupled with an increase in undirected functional connectivity, which we measure using correlation and coherence. This surprising opposite movement of directed and undirected measures is of more general interest for functional connectivity analyses, which we interpret using analytical modelling. Overall, our results uncover the neural dynamics of information flow in the psychedelic state, and highlight the importance of comparing multiple measures of functional connectivity when analysing time-resolved neuroimaging data.