Relative colour constancy is an essential requirement for many scientific imaging applications. However, most digital cameras differ in their image formations and native sensor output is usually inaccessible, e.g., in smartphone camera applications. This makes it hard to achieve consistent colour assessment across a range of devices, and that undermines the performance of computer vision algorithms. To resolve this issue, we propose a colour alignment model that considers the camera image formation as a black-box and formulates colour alignment as a three-step process: camera response calibration, response linearisation, and colour matching. The proposed model works with non-standard colour references, i.e., colour patches without knowing the true colour values, by utilising a novel balance-of-linear-distances feature. It is equivalent to determining the camera parameters through an unsupervised process. It also works with a minimum number of corresponding colour patches across the images to be colour aligned to deliver the applicable processing. Three challenging image datasets collected by multiple cameras under various illumination and exposure conditions, including one that imitates uncommon scenes such as scientific imaging, were used to evaluate the model. Performance benchmarks demonstrated that our model achieved superior performance compared to other popular and state-of-the-art methods.