This paper presents generic guidelines that English for Academic Purposes (EAP) tutors can use to guide them in the teaching of critical thinking in academic writing to (postgraduate) students in the UK. Based on interviews with 18 international master’s students and 14 content tutors based in a business school, school of education and institute of sport in a UK university, it found that while students tended to emphasise the process of critical writing, tutors tended to highlight the critical writing product. However, there was also crossover in their conceptualizations that emphasised four main reading-to-writing sub-skills involved in the process of critical academic writing: namely, developing a sceptical disposition towards academic reading, reading to understand disciplinary knowledge, reading to analyze and distinguish between less and more important information for note-taking purposes, and reading to evaluate literature. The key features of the critical writing product highlighted the importance of clear argumentation and student voice. These broad set of findings can be adapted and applied to EAP teaching through the use of Anderson et al.’s cognitive categories and processes and Toulmin’s argument pattern. Finally, the findings tended to support more generic patterns of critical academic writing across the disciplines in the study. More research is therefore needed to investigate how the conceptualization of critical thinking in academic writing varies between disciplines.