Although there are many studies of determinants of vegetarianism and veganism, there have been no previous studies of how their rates in a population jointly change over time. In this paper, we present a flexible model of vegetarian and vegan dietary choices, and derive the joint dynamics of rates of consumption. We fit our model to a pseudo-panel with 23 years of U.K. household data, and find that while vegetarian rates are largely determined by current household characteristics, vegan rates are additionally influenced by their own lagged value. We solve for equilibrium rates of vegetarianism and veganism, show that rates of consumption return to their equilibrium levels following a temporary event which changes those rates, and estimate the effects of campaigns to promote non-meat diets. We find that a persistent vegetarian campaign has a significantly positive effect on the rate of vegan consumption, in answer to an active debate among vegan campaigners.