Cameras are a core sensing modality in modern intelligent transportation systems (ITS), providing rich visual information on road-user activities. Multi-Camera Vehicle Tracking (MCVT) uses this data to reconstruct vehicle trajectories across camera networks, supporting applications such as traffic flow prediction and optimisation. However, most existing MCVT studies emphasise tracking accuracy while paying limited attention to real-time performance and scalability, both essential for real-world and city-scale deployment. To address this gap, we propose Edge-Assisted, Scalable and Efficient MCVT (EASE-MCVT), a distributed edge--server framework designed for real-time throughput and scalable operation. On the edge side, each camera stream is processed through object detection, single-camera tracking, geo-mapping and feature extraction, while only lightweight metadata, including vehicle locations and appearance features, is sent to the central server for cross-camera association. To improve both tracking accuracy and system efficiency, EASE-MCVT is optimised from algorithmic and system perspectives. Algorithmically, it introduces a dynamic workload scheme for tracklet-level feature extraction, a server-side re-match module to reconnect fragmented tracklets, and a self-supervised camera link model that learns spatio-temporal constraints to accelerate and stabilise cross-camera association. Systemically, it integrates production-oriented data engineering components to standardise deployment and data exchange for large-scale operation. To the best of our knowledge, EASE-MCVT is the first MCVT framework explicitly designed to address both real-time performance and scalability in a distributed edge--server setting. Experiments on the RoundaboutHD and CityFlow datasets demonstrate real-time throughput with competitive tracking accuracy, paving the way for city-wide real-time traffic management.