In recent years, academic debates about the productivity of 'knowledge' have been enriched by considerations of the productivity of 'non-knowledge' or 'ignorance.' A prominent example of this is Robert N. Proctor's seminal work Agnotology. The Making & Unmaking of Ignorance (2008), which contrasts the established field of epistemology (Proctor 2008, 1) with the "consequential" (2008, 2) effects ignorance has on our lives. In particular, Proctor focusses on "ignorance – or doubt or uncertainty – as something that is made, maintained and manipulated" (2008, 9). The aim of this paper is to extend the scope of non-knowledge to the concept of 'ambiguity,' hitherto neglected in this context, and to examine the productivity of ambiguity in relation to the use of Shakespeare within Brexit discourse. It will be argued that the ambiguity of Shakespeare's works, as well as the avoidance of that ambiguity, allowed for a use of the Bard for political gain. This will be contrasted with other examples of Brexit discourse, in which notions of ambiguity were embraced and related to Shakespeare's play The Tempest, which allowed for an aesthetic, more inclusive and forward-thinking approach to Brexit.