This article presents a new reduced order model for fast solutions to neutron transport problems. The novelty lies in the construction of optimal basis functions spanning the space-angle phase-space dimensions of the Boltzmann transport equation. Building on our previous work [1], it uses Proper Orthogonal Decomposition and the method of snapshots to form the reduced basis, but here a 2-stage construction is proposed that compresses the angle, then space, dimensions sequentially. The approach reduces the computational memory burden of processing the full discretised solutions of Boltzmann transport equation during the construction stage - a potential issue for large scale problems. The reduced model is both accurate and efficient to solve, and this is demonstrated by solving an eigenvalue and fixed source reactor physics problems with assumed uncertainties in nuclear cross-section data. Reductions in problem size and solving times exceeds 5 orders of magnitude in comparison to a full discretised model of similar accuracy. These gains would be expected to further increase for larger scale reactor problems.