Behavioural cloning (BC) is a commonly used imitation learning method to infer a sequential decision-making policy from expert demonstrations. However, when the quality of the data is not optimal, the resulting behavioural policy also performs sub-optimally once deployed. Recently, there has been a surge in offline reinforcement learning methods that hold the promise to extract high-quality policies from sub-optimal historical data. A common approach is to perform regularisation during training, encouraging updates during policy evaluation and/or policy improvement to stay close to the underlying data. In this work, we investigate whether an offline approach to improving the quality of the existing data can lead to improved behavioural policies without any changes in the BC algorithm. The proposed data improvement approach - Trajectory Stitching (TS) - generates new trajectories (sequences of states and actions) by `stitching' pairs of states that were disconnected in the original data and generating their connecting new action. By construction, these new transitions are guaranteed to be highly plausible according to probabilistic models of the environment, and to improve a state-value function. We demonstrate that the iterative process of replacing old trajectories with new ones incrementally improves the underlying behavioural policy. Extensive experimental results show that significant performance gains can be achieved using TS over BC policies extracted from the original data. Furthermore, using the D4RL benchmarking suite, we demonstrate that state-of-the-art results are obtained by combining TS with two existing offline learning methodologies reliant on BC, model-based offline planning (MBOP) and policy constraint (TD3+BC).