Background: Declining physical activity is associated with a rising burden of global disease. Efforts to reverse this trend have not been successful. We aimed to assess the efficacy of a facilitated behavioural intervention to increase the physical activity of sedentary individuals at familial risk of diabetes. Methods: We enrolled 365 sedentary adults who had a parental history of type 2 diabetes. They were recruited from either diabetes or family history registers at 20 general practice clinics in the UK. Eligible participants were randomly assigned to one of two intervention groups, or to a comparison group. All participants were posted a brief advice leaflet. One intervention group was offered a 1-year behaviour-change programme, to be delivered by trained facilitators in participants' homes, and the other the same programme by telephone. The programme was designed to alter behavioural determinants, as defined by the theory of planned behaviour, and to teach behaviour-change strategies. The principal outcome at 1 year was daytime physical activity, which was objectively measured as a ratio to resting energy expenditure. Analysis was by intention to treat. This study is registered as ISRCTN61323766. Findings: Of 365 patients, we analysed primary endpoints for 321 (88%) for whom we had data after 1 year of follow-up. At 1 year, the physical-activity ratio of participants who received the intervention, by either delivery route, did not differ from the ratio in those who were given a brief advice leaflet. The mean difference in daytime physical-activity ratio, adjusted for baseline, was -0·04 (95% CI -0·16 to 0·08). The physical-activity ratio did not differ between participants who were delivered the intervention face-to-face or by telephone (mean difference -0·05; 95% CI -0·19 to 0·10). Interpretation: A facilitated theory-based behavioural intervention was no more effective than an advice leaflet for promotion of physical activity in an at-risk group; therefore health-care providers should remain cautious about commissioning behavioural programmes into individual preventive health-care services.