Summary Background The UK lags behind many European countries in terms of cancer survival. Initiatives to address this disparity have focused on barriers to presentation, symptom recognition, and referral for specialist investigation. Selection of patients for further investigation has come under particular scrutiny, although preferences for referral thresholds in the UK population have not been studied. We investigated preferences for diagnostic testing for colorectal, lung, and pancreatic cancers in primary-care attendees. Methods In a vignette-based study, researchers recruited individuals aged at least 40 years attending 26 general practices in three areas of England between Dec 6, 2011, and Aug 1, 2012. Participants completed up to three of 12 vignettes (four for each of lung, pancreatic, and colorectal cancers), which were randomly assigned. The vignettes outlined a set of symptoms, the risk that these symptoms might indicate cancer (1%, 2%, 5%, or 10%), the relevant testing process, probable treatment, possible alternative diagnoses, and prognosis if cancer were identified. Participants were asked whether they would opt for diagnostic testing on the basis of the information in the vignette. Findings 3469 participants completed 6930 vignettes. 3052 individuals (88%) opted for investigation in their first vignette. We recorded no strong evidence that participants were more likely to opt for investigation with a 1% increase in risk of cancer (odds ratio [OR] 1·02, 95% CI 0·99–1·06; p=0·189), although the association between risk and opting for investigation was strong when colorectal cancer was analysed alone (1·08, 1·03–1·13; p=0·0001). In multivariable analysis, age had an effect in all three cancer models: participants aged 60–69 years were significantly more likely to opt for investigation than were those aged 40–59 years, and those aged 70 years or older were less likely. Other variables associated with increased likelihood of opting for investigation were shorter travel times to testing centre (colorectal and lung cancers), a family history of cancer (colorectal and lung cancers), and higher household income (colorectal and pancreatic cancers). Interpretation Participants in our sample expressed a clear preference for diagnostic testing at all risk levels, and individuals want to be tested at risk levels well below those stipulated by UK guidelines. This willingness should be considered during design of cancer pathways, particularly in primary care. The public engagement with our study should encourage general practitioners to involve patients in referral decision making. Funding The National Institute for Health Research Programme Grants for Applied Research programme.