Generative Artificial Intelligence (AI) has become a focal point in higher education worldwide. Research has demonstrated its potential to enhance student learning, particularly for those disadvantaged in traditional educational contexts. However, concerns regarding fairness, transparency, and the ethical use of technology underscore the importance of developing evidence-based guidelines and policies for governing generative AI. While global efforts have been made to create policies and support the ethical use of these tools, there remains a lack of data on student usage and attitudes toward generative AI tools to inform such policy-making. Specifically, the absence of cross-national perspectives on student use poses risks of widening the existing digital divide when implementing guidelines established by leading organizations, which often lack the voices of Global South contexts. Our study aims to use a cross-national survey to examine the current practices of GenAI in various national contexts. We are collecting data from several countries. So far, we have collected data from China (Hong Kong and Macau) and the UK and this paper reports the results from two countries. Our findings highlight three main themes comparing students' use and attitudes toward generative AI in learning between the UK and China: types of tools used, students' primary uses of the tools and associated concerns, and students' attitudes toward using the tools. Our results offer valuable insights into student use of generative AI worldwide and conclude with practical recommendations for policymakers and educational practitioners in the field of generative AI in higher education.