Online harms, such as hate speech, misinformation, harassment and self-harm promotion, continue to be widespread. While some work suggests that women are disproportionately affected by such harms, other studies find little evidence for gender differences in overall exposure. Here, we present preliminary results from a large, nationally representative survey of UK adults (N = 2000). We asked about exposure to 15 specific harms, along with fears surrounding exposure and comfort engaging in certain online behaviours. While men and women report seeing online harms to a roughly equal extent overall, we find that women are significantly more fearful of experiencing every type of harm that we asked about, and are significantly less comfortable partaking in several online behaviours. Strikingly, just 24% of women report being comfortable expressing political opinions online compared with almost 40% of men, with similar overall proportions for challenging certain content. Our work suggests that women may suffer an additional psychological burden in response to the proliferation of harmful online content, doing more 'safety work' to protect themselves. With much public discourse happening online, gender inequality in public voice is likely to be perpetuated if women feel too fearful to participate. Our results are important because to establish greater equality in society, we must take measures to ensure all members feel safe and able to participate in the online space.