This paper explores the possibility of the classroom as an exilic space of subversion in which we can pursue anarchist notions of personal transformation, relationships and society. Classroom environments in higher education institutions in Britain, particularly following the introduction of the Teaching Excellence Framework in September 2016, are premised upon relationships shaped by specific external standards: Employability, the instrumental pursuit of degrees, provider/consumer exchange, among others. Any notions of personal transformation are economic, and the broader goal is the pursuit of economic gain for individual, company and country. In an act of subversion of these external standards, I propose theorising the classroom as an exilic space: a temporally and spatially bracketed space in which participants and their relationships are not beholden to these various external referents. Instead, I put forward the exilic classroom as an anarchic space in which the interactions of the participants are not pre-defined but are formed in the process of the interactions themselves. In theorising the exilic classroom I draw on the work of Obika Gray, and push his notion of exilic space further by integrating the works of Michel de Certeau, Jamie Heckert and Gustav Landauer to help propose a classroom defined as a positive subversive everyday space that is not bound by its opposition to wider structures. The creation of such an exilic classroom assists the participants in stepping out of their expected roles as "provider" and "consumer", or "teacher" and "student", and allows the creation of a space of possibilities for our relationships