The recent increase in Open Access (OA) policies has brought forth important questions concerning the effect these policies have on the practice of publishing Open Access. In particular, is there evidence to support that mandating OA increases the proportion of OA outputs (in other words, do authors comply with relevant policies)? Furthermore, does mandating OA reduce the time from acceptance to the public availability of research outputs, and can compliance with OA mandates be effectively tracked? This work studies compliance with the UK REF 2021 Open Access policy. We use data from CrossRef and from CORE to create a dataset containing 1.6 million publications. We show that after the introduction of the UK OA policy, the proportion of OA research outputs in the UK has increased significantly, and the time lag between the acceptance of a publication and its Open Access availability has decreased, although there are significant differences in compliance between different repositories. We have developed a tool that can be used to assess publications' compliance with the policy based on a list of DOIs.