Equifocal submanifolds are an extension of the notion of isoparametric submanifolds in Euclidean spaces to symmetric spaces and consequently they share many of the properties well-known for their isoparametric relatives. An important step in understanding isoparametric submanifolds was Thorbergsson's proof of their homogeneity in codimension at least two which in particular solved the classification problem in this case. In this paper we prove the analogous result for equifocal submanifolds using the generalization of Thorbergsson's result to infinite dimensions due to Heintze and Liu.