This paper considers whether the different constitutional frameworks used to give structure to popular sovereignty, in the UK and Ireland, may be effective in precluding a ‘populist’ style of referendum use. In the wake of Brexit, it will consider whether the unstructured character of popular sovereignty in the UK Constitution encourages such a ‘populist’ style of referendum use, characterised by political discretion and elite instrumentalisation of the popular voice. However, drawing on the Irish experience, it will argue that constitutional law has a relatively modest capacity to regulate referendum-politics in the ways that many critics of the current UK framework see as being desirable. Thus it will argue that the ‘populist’ style of referendum use is not easily avoided by constitutional structure and regulation.