Generative AI has seen rapid development and adoption in educational settings, presenting both benefits and challenges for universities. This paper examines the response of UK universities, particularly the Russell Group of research-led universities, in developing policies and guidance on the use of generative AI. The analysis covers the implementation of the Russell Group's principles across member institutions, addressing areas such as academic integrity, assessment practices, student use, and guidance for staff. It also explores the varying levels of policy development at non-Russell Group universities, finding that some institutions may struggle to find resources for this issue. The paper situates these institutional responses within theoretical frameworks, highlighting how generative AI has disrupted established practices in higher education. It concludes by emphasizing the need for ongoing collaboration, policy development, and responsiveness to student perspectives as universities navigate this technology.