We present an experimental study of proton acceleration driven by femtosecond multi-PW lasers of three different prepulse parameters with the peak laser intensity of 1.2 × 1021 W/cm2 irradiating micrometre-thick metal foils. For 4-μm-thick copper foils, the highest-energy proton beam of 58.9 MeV is generated with the moderate-contrast laser, while the low-contrast or high-contrast lasers result in the lower proton cutoff energies. The one-dimensional hydrodynamic and two-dimensional particle-in-cell simulations indicate that the front preplasma of foils induced by the laser prepulse can enhance electron acceleration and in turn improve proton acceleration, while the rear preplasma will weaken the sheath field and be unfavourable for accelerating ions. For the case of the moderate contrast, the scale length of the front preplasma is long enough to generate high-temperature electrons compared to the high-contrast case, and the scale length of the rear preplasma is so short that the sheath field still remains strong compared with the low-contrast case, which is advantageous for generating high-energy protons. Meanwhile, a concrete map is theoretically given for accelerating higher-energy protons. This work extends the concept of the prepulse effect on target normal sheath acceleration (TNSA) to a wider range of laser parameters (multi-PW, 1021 W/cm2), representing an important step towards potential applications of TNSA-driven proton sources, especially considering that PW and even 10 PW laser facilities exist all around the world.