Exposure to fake news stories can result in false memories for the events portrayed, and this effect can be enhanced if the stories conform to the reader's ideological position. We exposed 1299 UK residents to fabricated news stories about Brexit. 44% of participants reported a false memory for at least one fabricated story, with a higher rate of false memories for stories that reflected poorly on the opposing side. This effect of ideological congruency was somewhat greater among participants who were exposed to a threat to their social identity as a Leave or Remain supporter; however, this moderating effect was only statistically significant in exploratory analyses using a more conservative definition of false memory. Participants with higher cognitive ability and analytical reasoning scores were less susceptible to false memories. Individuals with better knowledge about Brexit showed better discrimination between true and false stories, while self-reported engagement with the Brexit debate was associated with an increased tendency to "remember" any story, regardless of its truth. These results implicate a combination of social and individual factors in the development of false memories from fake news, and suggest that exposure to social identity threats may enhance the polarising effects of fake news.