Stabilisation of nonholonomic systems is of great practical importance to the industry. Moreover, fixed-time control is more comfortable than finite-time control since the upper bound of the settling time is independent on the initial system states in a fixed-time control issue and therefore can be estimated in advance. Inspired by the aforementioned two points, we consider the fixed-time stabilisation for a kind of uncertain nonholonomic systems subject to perturbations in this paper. A globally fixed-time stabilisation strategy is proposed by taking advantage of adding one power integrator technique and switching ideal. Under the designed controllers, all states can be regulated to zero before a fixed time and kept zero afterwards. As an application, the fixed-time stabilisation for a class of dynamic nonholonomic systems is also addressed by the combined method of adding one power integrator and terminal sliding-mode control. Three mechanical and academic examples are provided to show the flexibility and effectiveness of the assumptions and control algorithms.