Dialogue policy optimisation via reinforcement learning requires a large number of training interactions, which makes learning with real users time consuming and expensive. Many set-ups therefore rely on a user simulator instead of humans. These user simulators have their own problems. While hand-coded, rule-based user simulators have been shown to be sufficient in small, simple domains, for complex domains the number of rules quickly becomes intractable. State-of-the-art datadriven user simulators, on the other hand, are still domain-dependent. This means that adaptation to each new domain requires redesigning and retraining. In this work, we propose a domain-independent transformer-based user simulator (TUS). The structure of our TUS is not tied to a specific domain, enabling domain generalisation and learning of cross-domain user behaviour from data. We compare TUS with the state of the art using automatic as well as human evaluations. TUS can compete with rule-based user simulators on pre-defined domains and is able to generalise to unseen domains in a zero-shot fashion.