In this situation, do you have the right to overtake the vehicle in front of you to get across the railway crossing as swiftly as possible?

In the photo you are driving behind a dark car which is approaching a level crossing with half-barriers; on the right there is sign B-20 "STOP" with a plate "Sygnalizacja uszkodzona" (signals out of order), the half-barriers are up, and the roadway is divided by a double solid line. You are not entitled to overtake the vehicle in front to get across the level crossing faster. The answer is: no.

The Road Traffic Act prohibits a driver from overtaking a vehicle on a level crossing and immediately before it. The ban has no exceptions; "getting across faster" is no excuse at all - it is exactly rushing at level crossings that kills. By overtaking just before the tracks, you enter the lane for the opposite direction at a place where the vehicle in front of you may suddenly stop because it sees a train - the signals here are out of order; you, busy with the manoeuvre, will see this too late, and there may not be enough room to return to your lane. There is also sign B-20: the dark car is about to stop before the tracks, and by overtaking it you would cross without stopping. You stay behind it, stop when it stops, and cross the tracks only when it moves off and there is room on the other side.

Legal basis: Art. 28 para. 3 point 3 and para. 1 and 2 of the Road Traffic Act (Prawo o ruchu drogowym); § 21 para. 1 and 4 of the Regulation on road signs and signals