Online harms, such as hate speech, trolling and self-harm promotion, continue to be widespread. There are growing concerns that these harms may disproportionately affect women, reflecting and reproducing existing structural inequalities within digital spaces. Using a nationally representative survey of UK adults (N=1992), we examine how gender shapes exposure to a variety of online harms, fears surrounding being targeted, the psychological impact of online experiences, the use of safety tools, and comfort with various forms of online participation. We find that while men and women report roughly similar levels of absolute exposure to harmful content online, women are more often targeted by contact-based harms including image-based abuse, cyberstalking and cyberflashing. Women report heightened fears about being targeted by online harms, more negative psychological impact in response to online experiences, and increased use of safety tools, reflecting more engagement with personal safety work. Importantly, women also say they are significantly less comfortable with several forms of online participation, for example just 23% of women are comfortable expressing political views online compared to 40% of men. Explanatory models show direct associations between fears surrounding harms and comfort with particular online behaviours. Our findings show how online harms reinforce gender inequality by placing disproportionate psychological burden and participation constraints on women. These results are important because with much public discourse happening online, we must ensure all members of society feel safe and able to participate in online spaces.