Recently, the idea of a universal basic income has received unprecedented attention from policymakers, the media and the wider public. This has inspired a plethora of surveys that seek to measure the extent of public support for the policy, many of which suggest basic income is surprisingly popular. However, in a review of past surveys, with a focus on the UK and Finland, we find that overall levels of support for basic income can vary considerably. We highlight the importance of survey design and, by employing new survey data in each country, compare the levels and determinants of support for varied models of basic income. Our results point to the importance of the multi-dimensionality of basic income and the fragility of public support for the idea. The findings suggest that the ability of political actors to mobilise the public in favour of basic income will eventually depend on the precise model they wish to implement.