In this work, we address fast and agile manoeuvre control problem of unmanned aerial vehicles (UAVs) using an artificial neural network (ANN)-assisted conventional controller. Whereas the need for having almost perfect control accuracy for UAVs pushes the operation to boundaries of the performance envelope, safety and reliability concerns enforce researchers to be more conservative in tuning their controllers. As an alternative solution to the aforementioned trade-off, a reliable yet accurate controller is designed for the trajectory tracking of UAVs by learning system dynamics online over the trajectory. What is more, the proposed online learning mechanism helps us to deal with unmodelled dynamics and operational uncertainties. Experimental results validate the proposed approach and show the superiority of our method compared to the conventional controller for fast and agile manoeuvres, at speeds as high as 20m/s. An onboard implementation of the sliding mode control theory-based adaptation rules for the training of the proposed ANN is computationally efficient which allows us to learn system dynamics and operational variations instantly using a low-cost and low-power computer.