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Connected and automated vehicles (CAVs) represent a significant development in the transport industry owing to their intelligent and interconnected features. Potential field theory has been extensively used to model CAV driving behaviour owing to its objectivity, universality, and measurability. However, existing car-following models do not consider the impact of time delays and the influence of information from multiple vehicles ahead and behind. This paper focuses on the driving-safety risks associated with CAVs, aiming to enhance vehicle safety and reliability during travelling. We developed a multi-vehicle car-following model based on safety potential fields (MIDM-SPF), taking into account the characteristics of multi-vehicle connected information and time delays. To enhance the model's precision, real-world data from urban roads were employed, alongside an improved optimisation algorithm to fine-tune the car-following model. The simulation experiment revealed that MIDM-SPF significantly reduces stop-and-go traffic, thereby improving traffic flow stability in urban areas. Additionally, we validated the stability of our model under varying market penetration rates in large-scale mixed traffic. Our findings indicate that increasing the CAV proportion improves the stability of mixed traffic flows, which has important implications for alleviating traffic congestion and guiding the large-scale implementation of autonomous driving in the future. [ABSTRACT FROM AUTHOR]