A high penetration of electric vehicles (EVs) will deeply impact the management of electric power systems. To avoid costly grid reinforcements and the risk of load curtailment due to EV charging, indirect load control via adapted economic signals is a solution proposed by many utilities. Charging costs can be reduced with a domestic tariff applied only to EV charging using a dedicated load measurement method while enhancing the flexibility offered by EVs. We develop a game-theoretical model expressed and treated as a mathematical programme with equilibrium constraints (MPEC) to capture the interaction between a national regulatory authority (NRA) designing these tariffs and heterogeneous agents. First, we analyse the conditions in which EV-only tariffs can be applied for domestic slow charging sessions by comparing different energy profiles. Second, we study the impact of EV charging on different tariff structures to identify the most efficient way of recovering network costs. Submetering with a pure volumetric tariff can bring yearly gains varying from $64 to $110 compared to a flat rate. This depends on the share of investment in grid reinforcement that remains to be made. Finally, we derive policy implications from the results and earmark more sophisticated tariff designs for further investigation.