Virtual Reality Learning Environments (VRLEs) are a new form of immersive environments which are integrated with wearable devices for delivering distance learning content in a collaborative manner in e.g., special education, surgical training. Gaining unauthorized access to these connected devices can cause security, privacy attacks (SP) that adversely impacts the user immersive experience (UIX). In this article, we identify potential SP attack surfaces that impact the application usability and immersion experience, and propose a novel anomaly detection method to detect attacks before the UIX can be disrupted. Specifically, we apply: (i) machine learning techniques such as a multi-label KNN classification algorithm to detect anomaly events of network-based attacks that include potential threat scenarios of DoS (packet tampering, packet drop, packet duplication), and (ii) statistical analysis techniques that use a combination of boolean and threshold functions (Z-scores) to detect an anomaly related to application-based attacks (Unauthorized access). We demonstrate the effectiveness of our proposed anomaly detection method using a VRLE application case study viz., vSocial, specifically designed for teaching youth with learning impediments about social cues and interactions. Based on our detection results, we validate the impact of network and application based SP attacks on the VRLE UIX.