A new adaptive output feedback controller is given for a class of nonholonomic systems with non-vanishing external disturbances and nonlinear uncertainties. The non-vanishing disturbance is regarded as the generalised system state and an extended state observer (ESO) is designed for the uncertain external disturbance in order to ensure the global asymptotical stability of the closed loop system. A novel observer/estimator is constructed for auxiliary system states and unknown parameter estimates. The integrator backstepping recursive technique based on a construction rule is applied to the design of the output feedback adaptive controller. The simulation example for a mobile robot with velocity and angle velocity measured deviation and disturbance is given to validate the effectiveness of the proposed method.