Network Signalling Data (NSD) have the potential to provide continuous spatio-temporal information about the presence, mobility, and usage patterns of cell phone services by individuals. Such information is invaluable for monitoring large urban areas and supporting the implementation of decision-making services. When analyzed in real time, NSD can enable the early detection of critical urban events, including fires, large accidents, stampedes, terrorist attacks, and sports and leisure gatherings, especially if these events significantly impact mobile phone network activity in the affected areas. This paper presents empirical evidence that advanced NSD can detect anomalies in mobile traffic service consumption, attributable to critical urban events, with fine spatial (a spatial resolution of a few decameters) and temporal (minutes) resolutions. We introduce two methodologies for real-time anomaly detection from multivariate time series extracted from large-scale NSD, utilizing a range of algorithms adapted from the state-of-the-art in unsupervised machine learning techniques for anomaly detection. Our research includes a comprehensive quantitative evaluation of these algorithms on a large-scale dataset of NSD service consumption for the Paris region. The evaluation uses an original dataset of documented critical or unusual urban events. This dataset has been built as a ground truth basis for assessing the algorithms' performance. The obtained results demonstrate that our framework can detect unusual events almost instantaneously and locate the affected areas with high precision, largely outperforming random classifiers. This efficiency and effectiveness underline the potential of NSD-based anomaly detection in significantly enhancing emergency response strategies and urban planning. By offering a proactive approach to managing urban safety and resilience, our findings highlight the transformative potential of leveraging NSD for anomaly detection in urban environments.