This work considers the problem of distributed consensus tracking control of higher-order uncertain non-linear systems on a directed graph which contains a spanning tree with the leader node being the root. To facilitate controller design, in each agent of the network, a group of distributed and cascaded finite-time estimators is constructed for estimating the reference trajectory and its higher-order derivatives by information exchange among the local neighbours. Only the highest-order derivative estimator is discontinuous, whereas the estimators of the other reference states are continuous. Finite-time convergence property of each estimator is analysed. Then by utilising the estimated reference states, in each agent, a robust controller composed of some non-linear damping terms, a disturbance observer and a sliding mode control term is designed, so that the agent's states track the estimated reference states with an arbitrarily small ultimate error bound. The tracking performance is theoretically analysed. And simulation examples are provided to demonstrate the performance of the finite-time reference estimators and the tracking controllers.