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This paper studies the distributed cooperative control problem for multiple surface vessels (MSVs) subject to unknown environmental disturbances, model uncertainties, unavailable velocities and prescribed performance constraints. Firstly, a fixed-time extended state observer (FxESO) is designed to provide the estimations of velocities and lumped disturbances (including unknown environmental disturbances and model uncertainties). Secondly, to improve the convergence performance of the MSVs, a hyperbolic cosecant prescribed performance function is incorporated into the cooperative control algorithm. Thirdly, a fixed-time event-triggered control law with prescribed performance constraint is applied to cooperative control based on a fixed-time nonsingular terminal sliding mode manifold (FxNTSMM), and the cooperative errors can converge within fixed time. Finally, by employing Lyapunov function theory, the stability of the closed-loop system is analyzed. Simulation results are given to demonstrate the effectiveness of the proposed control scheme.