This study addresses an efficient algorithm for joint estimation of the two-dimensional (2D) angles and polarisations of the signals impinging on a planar array of co-centred crossed dipole pairs. Based on a novel multi-layered signal decomposition scheme, the proposed algorithm estimates 2D angles and polarisations alternatively in a coarse-to-fine manner by progressively decomposing the signals into finer groups using an angle- or polarisation-based beamforming process. Such a decomposition not only partitions the signals with close parameters into separate groups, but it also reduces the power of the noise, both of which can in turn enhance the estimation accuracy. Moreover, the data are properly stacked in each stage by exploiting the intrinsic data structures so that only the 1D estimation of signal parameters via rotational invariance techniques algorithms are required, thus entailing lower computational load. Conducted simulations show that the performance of the proposed algorithm is close to that of previous works, but its computational complexity is substantially lower and is free of pairing of the estimated parameters with the multi-layered parameter estimation scheme.