Information privacy is a critical design feature for any exchange system, with privacy-preserving applications requiring, most of the time, the identification and labelling of sensitive information. However, privacy and the concept of “sensitive information” are extremely elusive terms, as they are heavily dependent upon the context they are conveyed in. To accommodate such specificity, we first introduce a taxonomy of four context classes to categorise relationships of terms with their textual surroundings by meaning, interaction, precedence, and preference. We then propose a predictive context-aware model based on a Bidirectional Long Short Term Memory network with Conditional Random Fields (BiLSTM + CRF) to identify and label sensitive information in conversational data (multi-class sensitivity labelling). We train our model on a synthetic annotated dataset of real-world conversational data categorised in 13 sensitivity classes that we derive from the P3P standard. We parameterise and run a series of experiments featuring word and character embeddings and introduce a set of auxiliary features to improve model performance. Our results demonstrate that the BiLSTM + CRF model architecture with BERT embeddings and WordShape features is the most effective (F1 score 96.73%). Evaluation of the model is conducted under both temporal and semantic contexts, achieving a 76.33% F1 score on unseen data and outperforms Google’s Data Loss Prevention (DLP) system on sensitivity labelling tasks.