Continuous carbon-fibre (CCF) additive manufacturing of composites has significant potential for production of optimised structures. However, stiffness and strength in parts are often significantly lower than manufacturer material data. For thermoset-impregnated CCF, post-consolidation of specimens has greatly increased strength. In this contribution, the effect of post-consolidation for thermoplastic CCF material is presented. Specimens were manufactured on a commercial AM CCF printer and post-consolidation was performed by rapid compression moulding. Porosity was evaluated by X-ray Computed Tomography (CT) and a significant reduction from 5.3 vol.% to 1.1 vol.% was yielded. Experimental testing is performed in four-point bending with as-printed and post-consolidated samples. Bending stiffness and strength data was obtained. The results show that the bending strength was below expectations in as-printed specimens. Finite Element Analysis indicates that snap-buckling of a small number of outer layers can lead to such a reduced apparent bending strength, and CT scans of fracture surfaces of as-printed specimens reveal the presence of interlaminar debonding. It is shown that post-consolidation highly improves the interlaminar bond, yielding experimentally obtained strength values close to nominal material strength, and the expected kink-band compressive failure is achieved.