This paper considers whether the impact agenda that has developed over the last decade in UK universities is likely to help create the conditions in which critical educational research makes a more visible difference to society. The UK audit of university research quality (the research excellence framework (REF) now includes an assessment of impact. Impact pathways are requirements of both national and European Union research funding bodies and the Australian Research Council. Issues in the assessment of the social impact of research are explored by the European projects Evaluating the impact of EU SSH, social science humanities, research (IMPACT-EV) and ACcelerate CO-creation by setting up a Multi-actor Platform for Impact from Social Sciences and Humanities (ACCOMPLISSH). For many UK researchers the institutional focus on influencing the world outside the academy has brought welcome support and resources to engage with society and may appear to bring universities back to something approaching their original civic identity. However, evidence from across the academy suggests that impact as depicted in REF impact case studies does not accurately represent the experience either of the academic research endeavour or of impact as it may be more broadly construed. Analysis reported here of 85 highly rated impact case studies in the education unit of assessment of the 2014 REF suggests there is a risk that the REF impact process will embed a shift against qualitative and theoretically driven methodology that is often found in socially critical educational research. Impact is postured as neutral, hiding the neoliberal drive towards research models based on implementation, evaluation and policy. There is a need to create spaces in universities for rethinking of the impact agenda, perhaps looking at value or social creation instead of, or as an integral aspect of, impact.