Modern laser technology is now sufficiently advanced that collisions between high-intensity laser pulses and laser-wakefield-accelerated (LWFA) electron beams can reach the strong-field regime, so that it is possible to measure the transition between the classical and quantum regimes of light–matter interactions. However, the energy spectrum of LWFA electron beams can fluctuate significantly from shot to shot, making it difficult to clearly discern quantum effects in radiation reaction (RR), for example. Here we show how this can be accomplished in only a single laser shot. A millimetre-scale pre-collision drift allows the electron beam to expand to a size larger than the laser focal spot and develop a correlation between transverse position and angular divergence. In contrast to previous studies, this means that a measurement of the beam's energy-divergence spectrum automatically distinguishes components of the beam that hit or miss the laser focal spot and therefore do and do not experience RR.