During extreme space weather events the fluctuating geomagnetic field induces an electric field in the conducting Earth. This geoelectric field in turn generates currents in ground‐based technological systems, affecting their operation. Thus, calculation of the geoelectric field is a key step in predicting, assessing, and, potentially, forecasting the space weather impact on critical infrastructure. We present an approach and a tool for the first fully coupled regional three‐dimensional (3‐D) forward modeling of the electromagnetic field from far geospace down to the surface of the Earth. Applying the developed tool to the British Isles, we perform a 3‐D study in order to explore in detail the so‐called coastal effect (i.e., the anomalous behavior of the geoelectric field near the coasts) and to understand the limitations of the thin‐sheet model widely used for estimating this effect. For this purpose we compare the results of 3‐D and thin‐sheet modelings for plane wave source of excitation and different periods of variations. We conclude that for the British Isles the thin sheet is a reasonable approximation for periods longer than a few minutes. However, for shorter periods 3‐D modeling is essential. Another inference from the results of 3‐D modeling for plane wave and realistic sources is that for the British Isles the geoelectric field is distorted by the coastal effect practically everywhere on land. Finally, we compare modeled and observed geomagnetic fields at four observatories in the region during the first day of the Halloween storm in 2003 and discuss the results of this comparison.