Background: In Australia, despite the success of tobacco control policy interventions, policymakers remain resistant to policy-based approaches to diet, alcohol, physical inactivity and obesity, concerned about community perceptions of such interventions as “nanny-statist”. We examined how people’s general positions on government intervention related to their positions on different preventive policy options. Methods: Data were from a 2018 nationally representative cross-sectional telephone survey of 2601 Australian adults. Survey questions related to endorsement of different conceptualisations of government intervention (nanny state, paternalistic, shared responsibility and communitarian) and support for specific health interventions, using forced-choice questions about preferences for individual/treatment measures versus population/preventive health measures. We analysed associations between scores on different conceptualisations of government intervention and support of different policy options for tobacco and diet, and preferences for prevention over treatment. Results: The Nanny State Scale showed an inverse relationship with support for tobacco- and diet-related interventions, and alternative conceptualisations (paternalistic, shared responsibility and communitarian) showed a positive relationship. Effect sizes in all cases were small. Those aged 55+ demonstrated greater support for policy action on tobacco and diet, and greater preference for systemic rather than individual-level interventions. Conclusion: General disposition towards government intervention, although correlated with support for specific policy actions, is not deterministic.