This paper investigates how changes in hospital choice sets affect levels of patient demand for elective hospital care. We exploit a set of reforms in England that opened up the market for publicly-funded patients to private hospitals. Impacts on demand are estimated using variation in distance to these private hospitals, within regions where supply constraints are fixed. We find that the reforms increased demand for publicly-funded procedures. For public hospitals, volumes remained unchanged but waiting times fell. Taken together, our results provide new insights into how individuals make choices about their care and the scope of competition between hospitals.