The magnetic field driven superconductor/insulator transition is studied in a large variety of La2−xSrxCuO4 thin films of various Sr dopings. Temperature dependence of the resistivity down to 4.2 or 1.5 K under high pulsed magnetic field (up to 57 T) is analyzed. In particular, the existence of plateaus in the resistance versus temperature curves, in a limited range of temperature, for given values of the magnetic field is carefully investigated. It is shown to be associated to scaling behaviour of the resistance versus magnetic field curves, evocative of the presence of a quantum critical point. A three-dimensional (H,x,T) phase diagram is proposed, taking into account the intrinsic lamellar nature of the materials by the existence of a temperature crossover from quantum-two-dimensional to three-dimensional behavior.