A high penetration of electric vehicles (EVs) will deeply impact the management of electric power systems. The risk of not providing adapted EV pricing signals can lead to inefficient investments in grid infrastructure. To avoid costly grid reinforcements and to ensure proper guidance for EV charging, a solution allowing customers to access EV-only rates without installing a separate meter, which we refer to as submetering, is an attractive option for EV owners and grid operators. We develop a game-theoretical model expressed and treated as a mathematical program with equilibrium constraints (MPEC) to capture the interaction between a national regulatory authority (NRA) designing these tariffs and heterogeneous agents. This framework represents a stylized regulatory setup applicable to several European countries. First, we analyse the conditions in which EV-only tariffs can be applied for domestic charging 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. We found that the adoption of submetering under a pure volumetric tariff can bring yearly gains varying from $ 64 to $ 125 to consumers with EV. Finally, we derive policy implications from the results.