An increasing share of electric vehicles can mean excessive peak loads in low-voltage power distribution networks. Introducing peak shaving mechanisms to the charging systems, such overloads can be mitigated significantly. The first contribution of this study is to quantify the amount of flexibility that electric vehicles can contribute to peak load reduction so that the drivers can still fully charge the batteries of their vehicles. The second contribution is that the study presents and compares two optimisation strategies for peak load reduction. The work is based on real charging data covering about 25,000 charging sessions at various charging sites in the metropolitan area of the Finnish capital city. The main finding is that the peak loads at charging sites can be reduced by up to 55%. Another important result is that load reduction through low-power charging is achievable only if the average parking time at the charging site is >3 h, without affecting the user experience negatively. It is also found out that the average parking time is over 2 h longer than the average charging time, which indicates the enormous potential of electric vehicles in peak shaving.