Composite filament co-extrusion (CFC) additive manufacturing (AM) is a bi-matrix rapid fabrication technique that is used to produce highly customisable composite parts. By this method, pre-cured, thermoset-based composite carbon fibre (CCF) is simultaneously extruded along with thermoplastic (TP) binding melt as the matrix. Like additive manufacturing, CFC technology also has inherent challenges which include voids, defects and a reduction in CCF’s volume in the fabricated parts. Nevertheless, CFC AM is an emerging composite processing technology, a highly customisable and user-oriented manufacturing unit. A new TP-based composites processing technique has the potential to be synergised with conventional processing techniques such as injection moulding to produce lightweight composite parts. Thus, CFC AM can be a credible technology to replace unsustainable subtractive manufacturing, if only the defects are minimised and processing reliability is achieved. The main objective of this research is to investigate and reduce internal voids and defects by utilising compression pressing as a rapid consolidation post-processing technique. Post-processing techniques are known to reduce the internal voids in AM-manufactured parts, depending on the TP matrices. Accordingly, the rapid consolidated neat polylactic acid (PLA) TP matrix showed the highest reduction in internal voids, approximately 92%. The PLA and polyamide 6 (PA6) binding matrix were reinforced with short carbon fibre (SCF) and long carbon fibre (LCF), respectively, to compensate for the CCF’s fibre volume reduction. An increase in tensile strength (ca. 12%) and modulus (ca. 30%) was observed in SCF-filled PLA. Furthermore, an approximately 53% increase in tensile strength and a 76% increase in modulus for LCF-reinforced PA6 as the binding matrix was observed. Similar trends were observed in CFC and rapidly consolidated CFC specimens’ flexural properties, resulting due to reduced internal voids.