Accurate segmentation of brain tumours images is crucial for diagnosis, treatment planning, and monitoring of disease progression. However, acquiring sufficient medical imaging data for deep learning models is challenging, especially when sharing data across institutions is not feasible due to legal, privacy, and technical concerns. In this work, we propose federated learning techniques with a 3D U-Net deep model on the BraTS 2020 dataset to segment the brain tumour lesions without sharing patient data. Our federated semantic segmentation model achieved high Dice similarity coefficients of 0.861, 0.826, and 0.803, and Hausdorff distances (95%) of 25.161, 9.419, and 8.792 mm for the whole tumour, tumour core, and enhancing tumour core, respectively. These results were comparable to those of the centralized model, which achieved similar Dice similarity coefficients and Hausdorff distances. Furthermore, our quantitative results on the final test set demonstrate that our solution exhibited remarkable performance, achieving Dice scores of 0.896, 0.873, and 0.868, accompanied by Hausdorff distances (95%) of 23.611, 12.208, and 11.088 mm. This study highlights the potential of multi-institutional federated learning for brain tumour segmentation and its implications for data privacy preservation in medical imaging.