Scientific institutions are increasingly embracing values of inclusivity and public engagement, but how do these two dimensions intersect? Science festivals have rapidly expanded in recent years as an outgrowth of these values, aiming to engage and educate the public about scientific topics and research. While resources invested in public engagement by scientists, universities, and governments are admirable in principle; this study indicates that their ambition to broaden the reach of science may be going unrealized in practice. Using data from three major UK science festivals, we demonstrate such events are disproportionately reaching economically privileged and educated audiences already invested in science, as opposed to diverse and broadly representative samples of the general public. Our results demonstrate that these science festivals are falling short of their aims to make science accessible to a broad audience. There is a clear need for improved practices and on-going evaluation to ensure science festivals include those who are not already scientifically converted.