This study investigates the influence of generative artificial intelligence (GAI), specifically AI text generators (ChatGPT), on critical thinking skills in UK postgraduate business school students. Using Bloom's taxonomy as theoretical underpinning, we adopt a mixed-method research employing a sample of 107 participants to investigate both the influence and challenges of these technologies in higher education. Our findings reveal that the most significant improvements occurred at the lower levels of Bloom's taxonomy. We identify concerns relating to reliability, accuracy, and potential ethical implications of its application in higher education. The significance of this paper spans across, pedagogy, policy and practice, offering insights into the complex relationship between AI technologies and critical thinking skills. While highlighting the multifaceted aspects of the impact of AI in education, this article serves as a guide to educators and policymakers, stressing the importance of a comprehensive approach to fostering critical thinking and other transferable skills in the higher education landscape.