We ask how to defend user ability to plausibly deny their interest in topics deemed sensitive in the face of search engine learning. We develop a practical and scalable tool called \PDE{} allowing a user to detect and assess threats to plausible deniability. We show that threats to plausible deniability of interest are readily detectable for all topics tested in an extensive testing program. Of particular concern is observation of threats to deniability of interest in topics related to health and sexual preferences. We show this remains the case when attempting to disrupt search engine learning through noise query injection and click obfuscation. We design a defence technique exploiting uninteresting, proxy topics and show that it provides a more effective defence of plausible deniability in our experiments.