Electric Vehicles (EVs) have gained large interest in the energy sector as a carrier to support clean transportation and green electricity. The potential to use battery storages of electric vehicles as a sink for excess electricity that may result from large integration of wind power, especially in countries like Denmark, is widely discussed and promoted. However, the wide-spread adoption of EVs requires the provision of intelligent grid and EV charging infrastructure. To analyse and understand the amount of EVs that could be integrated in the local distribution grids, within its existing capabilities, is absolutely essential for the system operators to plan and implement the levels of grid reinforcement and intelligence required. This paper investigates the local grid limitations to accommodate large amount of EVs of sizable power ratings in residential areas. The case study applied in this paper uses a detailed secondary distribution grid model in Denmark. Various EV integration scenarios are analysed in this work to understand the network operational flexibility and ruggedness. The simulation results show that level of EV integration varies with the strength of different feeders in the studied network. Simple grid reinforcement measures like adding new feeders in the existing network improves EV penetration levels.