Waiting time for elective treatments is a major health policy issue in many OECD countries that was exacerbated by COVID-19. We test whether waiting times from referral to surgery reduces post-operative health and resource use for patients in need of a hip or knee replacement in England. We employ a large administrative dataset for 2015/16-2022/23. We use an instrumental-variable regression approach based on congestion while controlling for a rich set of patient characteristics and hospital fixed effects. We find that, for public hospitals in the pre-COVID period (April 2015-January 2020), referral-to-treatment waiting times do not have a statistically significant effect on post-operative health for either hip or knee replacement (as measured by Oxford Hip or Knee Score) or the probability of being readmitted within 28 days following discharge. However, for public hospitals, one additional month of waiting instead increases length of stay by 0.075 days (2.06%) for hip replacement but has no effect for knee replacement. For private hospitals, we do not find an effect between referral-to-treatment waiting times and any of the outcomes. In heterogeneity analysis, we generally do not find differential effects of waiting on different groups (by gender, ethnicity, income and education deprivation, pre-operative health). In the COVID-19 period (April 2020-March 2023), we generally do not find an effect of waiting times on any of the outcomes.