Exposure to 'fake news' can result in false memories, with possible consequences for downstream behaviour. Given the sharp rise in online misinformation during the coronavirus pandemic, it is important to understand the factors that influence the development of false memories. The present study measured susceptibility to false memories following exposure to fabricated news stories about the pandemic in a sample of 3746 participants. We investigated the effect of individual differences in (1) knowledge about COVID-19, (2) engagement with media or discussion about the coronavirus, (3) anxiety about COVID-19 and (4) analytical reasoning. Notably, objectively and subjectively assessed knowledge about COVID-19 were not significantly correlated. Objectively assessed knowledge was associated with fewer false memories but more true memories, suggesting a true discrimination between true and fake news. In contrast, participants who merely believed themselves to be very knowledgeable were more likely to report a memory for true stories, but showed no reduction in false memories. Similarly, individuals who reported high levels of media engagement or anxiety about COVID-19 reported an increase in true (but not false) memories. Finally, higher levels of analytical reasoning were associated with fewer memories for both true and fabricated stories, suggesting a stricter threshold for reporting a memory for any story. These data indicate that false memories can form in response to fake COVID-19 news and that susceptibility to this misinformation is affected by the individual's knowledge about and interaction with COVID-19 information, as well as their tendency to think critically.