Aims. The main goal of this paper is to present an accurate and efficient numerical strategy for solving the radiative transfer problem for polarised radiation in strong resonance lines forming out of local thermodynamic equilibrium while taking angle-dependent partial frequency redistribution (PRD) effects and J-state interference into account. We considered the polarisation produced both by the Zeeman effect and by the scattering of anisotropic radiation along with its sensitivity to the Hanle and magneto-optical effects. Methods. We introduce a formalism that allows for treating both a two-level and a two-term atom in the presence of arbitrary magnetic and bulk velocity fields. The problem is formulated by treating the population of the lower level or term as a fixed input parameter. This approach makes the problem linear with respect to the radiation field, enabling the application of efficient matrix-free preconditioned iterative methods for its solution. Additionally, the computation of the scattering emissivity in the co-moving frame, together with a careful choice of the angular and spectral quadrature nodes, allowed us to speed up the calculations by reducing the number of evaluations of the redistribution functions. Results. We applied the proposed solution strategy in order to synthesise the Stokes profiles of the Mg II h&k doublet and the H I Ly-α line in 1D semi-empirical models. The results demonstrate that the method is both fast and accurate. A comparison with calculations from HanleRT-TIC displayed an overall good agreement, thereby validating our solution strategy. Moreover, for the wavelength-integrated polarisation profiles of the H I Ly-α line, we found an excellent agreement between the results obtained including PRD effects in their general angle-dependent description and those obtained considering the angle-averaged simplifying approximation.