One way to encourage the usage of electric vehicles (EVs) is to reduce the connection time by using higher-powered charging points at home. Nonetheless, a massive adoption of this technology could increase the network power requirements, stressing the grid beyond the technical limits. Therefore, it is important to assess how much the aggregate power will increase compared to the slow-charging process and how to minimize it. Hence, an EV charging coordination model is developed to compare the impact on the system demand of residential slow and fast-charging plans by minimizing the maximum aggregate demand. Here, “slow” and “fast” correspond to the minimum and the maximum charging speeds for 1-phase, mode 3 of the IEC 61851-1. To create an accurate model, realistic UK load profiles, real EV energy requirements, and real travel statistics of car drivers in the UK were included. Additionally, the stochasticity of customers was incorporated by solving the optimization for thousands of different groups of households and EVs. The results indicate that due to the greater flexibility of fast-charging events, if no coordination is considered, the aggregate effects increase by 15% compared to the slow-charging case. However, if the process is coordinated, nearly the same maximum aggregate demand is found regardless of whether the charging is fast or slow.