The social transmission of information is critical to the emergence of animal culture. Two processes are predicted to play key roles in how socially-transmitted information spreads in animal populations: the movement of individuals across the landscape and conformist social learning. We develop a model that, for the first time, explicitly integrates these processes to investigate their impacts on the spread of behavioural preferences. Our results reveal a strong interplay between movement and conformity in determining whether locally-variable traditions establish across a landscape or whether a single preference dominates the whole population. The model is able to replicate a real-world cultural diffusion experiment in great tits Parus major, but also allows for a range of predictions for the emergence of animal culture under various initial conditions, habitat structure and strength of conformist bias to be made. Integrating social behaviour with ecological variation will be important for understanding the stability and diversity of culture in animals.