Underwater fish segmentation to estimate fish body measurements is still largely unsolved due to the complex underwater environment. Relying on fully-supervised segmentation models requires collecting per-pixel labels, which is time-consuming and prone to overfitting. Self-supervised learning methods can help avoid the requirement of large annotated training datasets, however, to be useful in real-world applications, they should achieve good segmentation quality. In this paper, we introduce a Transformer-based method that uses self-supervision for high-quality fish segmentation. Our proposed model is trained on videos -- without any annotations -- to perform fish segmentation in underwater videos taken in situ in the wild. We show that when trained on a set of underwater videos from one dataset, the proposed model surpasses previous CNN-based and Transformer-based self-supervised methods and achieves performance relatively close to supervised methods on two new unseen underwater video datasets. This demonstrates the great generalisability of our model and the fact that it does not need a pre-trained model. In addition, we show that, due to its dense representation learning, our model is compute-efficient. We provide quantitative and qualitative results that demonstrate our model's significant capabilities.