Within the context of eye-gaze tracking, the capability of permitting the user to move naturally is an important step towards allowing for more natural user interaction in less constrained scenarios. Natural movement can be characterised by changes in head pose, as well as non-rigid face deformations as the user performs different facial expressions. While the estimation of head pose within the domain of eye-gaze tracking is being increasingly considered, the face is most often regarded as a rigid body. The few methods that factor the challenge of handling face deformations into the head pose estimation problem, often require the availability of a pre-defined face model or a considerable amount of training data. In this paper, we direct our attention towards the application of shape-and-motion factorisation for head pose estimation, since this does not generally rely on the availability of an initial face model. Over the years, various shape-and-motion factorisation methods have been proposed to address the challenges of rigid and non-rigid shape and motion recovery, in a batch or sequential manner. However, the real-time recovery of non-rigid shape and motion by factorisation remains, in general, an open problem. Our work addresses this open problem by proposing a sequential factorisation method for non-rigid shape and motion recovery, which does not rely on the availability of a pre-defined face deformation model or training data. Quantitative and qualitative results show that our method can handle various non-rigid face deformations without deterioration of the head pose estimation accuracy.