A first-principles theoretical investigation of positron annihilation in alkali halide crystals is carried out using a simplified cluster-embedding scheme. The system is represented as a halide-centred cluster with basis functions only at the centre. The rest of the crystal is modelled in two ways: (i) point ions located at lattice positions; and (ii) frozen-orbital ions derived from an energy band calculation for the pure crystal. Calculations for both models are carried out within the self-interaction-corrected local spin-density approximation and by incorporating an electron - positron correlation functional. The effect of the model assumed on the calculated positron lifetimes is analysed by demonstrating the sensitivity of the results to the inclusion of the Madelung potential. A comparison of positron lifetimes of the ground state of the positron to lifetime components identified in experimental work on lithium and sodium halide systems is made.