The Prevent counter terrorism strategy ('Prevent') -- specifically the duty to report those deemed vulnerable to, or causing suspicions of, radicalisation -- has been intensely criticised within UK higher education for its racialised and colonial agenda; its potential to curb academic freedom; and its reframing of the pedagogical dynamic as one of surveillance. A specific concern is that Prevent limits possibilities for critical teaching and learning which is predicated on notions of openness and mutual exchange. This paper responds to the claim that Prevent and the statuary duty it implies, "prevents" critical thinking using empirical data collection with 14 academic faculty teaching Politics across 4 English universities. These data reveal how Prevent's effects are neither uniform nor straightforward but that its bureaucratic and legalistic framing produces significant and detrimental 'critical closures' with an urgent need for higher education institutions to approach future guises of Prevent both critically and pedagogically.