In this paper we present methods for estimating shape from polarisation and shading information, i.e. photo-polarimetric shape estimation, under varying, but unknown, illumination, i.e. in an uncalibrated scenario. We propose several alternative photo-polarimetric constraints that depend upon the partial derivatives of the surface and show how to express them in a unified system of partial differential equations of which previous work is a special case. By careful combination and manipulation of the constraints, we show how to eliminate non-linearities such that a discrete version of the problem can be solved using linear least squares. We derive a minimal, combinatorial approach for two source illumination estimation which we use with RANSAC for robust light direction and intensity estimation. We also introduce a new method for estimating a polarisation image from multichannel data and provide methods for estimating albedo and refractive index. We evaluate lighting, shape, albedo and refractive index estimation methods on both synthetic and real-world data showing improvements over existing state-of-the-art.