•The second magnetization peak (SMP) in La2−xSrxCuO4 single crystals disappears completely in the doping range of well developed static stripe order (x ∼ 1/8) when the external magnetic field is perpendicular to the stripe plane.•The SMP evolution with decreasing doping follows the instability of the Bragg vortex glass detected in small-angle neutron scattering experiments.•Our analysis supports the scenario in which the SMP is generated by the pinning-induced disordering of the Bragg vortex glass in the dynamic conditions of dc magnetic measurements. The occurrence of a second magnetization peak (SMP) on the dc magnetization curves of superconducting single crystals with random quenched disorder in increasing external magnetic field H is quite common. Many models for this intriguing phenomenon have been proposed so far, but its origin is still under strong debate. Optimally doped and overdoped La2−xSrxCuO4 single crystals (x ≥ 0.15) exhibit an SMP over a large temperature interval, up to very close to the critical temperature. By decreasing doping, it was found that with H oriented along the c axis the SMP completely disappears in the doping domain of well developed static charge and spin stripes (x ∼ 1/8), reappearing for x ≤ 0.10. This behaviour follows the instability of the Bragg vortex glass generated by the static stripe order (as revealed by small-angle neutron scattering experiments), which is confirmed by our magnetization relaxation measurements. If H is along the (a, b) planes, the SMP is observed for all investigated specimens. The presented analysis supports the scenario in which the SMP is generated by the pinning-induced disordering of the low-field Bragg vortex glass in the dynamic conditions of dc magnetic measurements.