In this paper, we show that the widely accepted methodology for the assessment of risk perception - Likert-type survey questions featuring a set of risks with fixed response alternatives measuring the extent of worry or concern - may overestimate food risk perception. Using a European representative sample survey (n=26,961) that included an open-ended question asking about problems and risks with food and eating, followed by a battery of closed questions (CQs) assessing food risk perception, we find a similar ranking of perceived food risks across the two methods. Across Europe, the five priority concerns are chronic food-related illness; food origins and quality; acute food-related illness; chemical contamination; and adulteration of food. However, the discrepancies between mentioning a risk in the open-ended question and the expression of worry about risks in the CQ are substantial. Of those who did not mention a specific risk category in the open question, between 60 and 83% (depending on risk category) expressed worry in the CQ. This parallels previous research on the fear of crime, showing that survey responses lead to greatly inflated estimates of the public's fear of crime than is evidenced by qualitative questioning. It is also consistent with evidence from research on cognitive aspects of survey methodology, suggesting that survey questions may frame the respondent's thinking about an issue. We conclude with recommendations for the use of branched questions in the quantitative elicitation of public perceptions of risk.