Objective: The objective of this paper is to analyse the extent to which electric vehicle (EV) charging control substitutes the needs for cross-border electricity transmission investment. Method: EUPowerDispatch, a minimum-cost unit commitment dispatch model, is used to compare the impacts of controlled EV charging and cross-border transmission for different levels of variable renewable energy sources penetration in two case studies: a conceptual two-node system and the European power system. Results: Results show how both controlled EV charging and cross-border transmission capacity reduce electricity dispatch costs, curtailment of variable renewable energy sources (RES), storing energy by utilising pumped hydro, and unserved load. The paper shows that when the demand for arbitrage is low, controlled EV charging can substitute for a certain volume of cross-border transmission capacity. When demand for arbitrage becomes higher due to higher volumes of RES, the two increasingly complement one another with respect to reducing dispatch costs. The main reason for this is that cross-border transmission capacity is needed to transport power to where electric vehicles can absorb it. Conclusion: Demand response, in this case EV charging control, is not only a competitor of cross-border electricity transmission. In the presence of a high volume of RES, they can complement one another. Practical implications: The study presented in this paper provides insights about potential investment decisions that Europe will have to face in order to meet the decarbonisation goals set by the European Commission by 2050. Transmission planners should take into consideration that while demand response and cross-border transmission capacity may substitute each other at a limited share of intermittent renewable energy, at a higher share their interactions become more complex as their benefits become dependent on each other.