We introduce a novel neural network architecture -- Spectral ENcoder for SEnsor Independence (SEnSeI) -- by which several multispectral instruments, each with different combinations of spectral bands, can be used to train a generalised deep learning model. We focus on the problem of cloud masking, using several pre-existing datasets, and a new, freely available dataset for Sentinel-2. Our model is shown to achieve state-of-the-art performance on the satellites it was trained on (Sentinel-2 and Landsat 8), and is able to extrapolate to sensors it has not seen during training such as Landsat 7, PerúSat-1, and Sentinel-3 SLSTR. Model performance is shown to improve when multiple satellites are used in training, approaching or surpassing the performance of specialised, single-sensor models. This work is motivated by the fact that the remote sensing community has access to data taken with a hugely variety of sensors. This has inevitably led to labelling efforts being undertaken separately for different sensors, which limits the performance of deep learning models, given their need for huge training sets to perform optimally. Sensor independence can enable deep learning models to utilise multiple datasets for training simultaneously, boosting performance and making them much more widely applicable. This may lead to deep learning approaches being used more frequently for on-board applications and in ground segment data processing, which generally require models to be ready at launch or soon afterwards.