High-viscosity liquid cis-1,4 polyisoprene (PI), with up to 20 wt% single-wall carbon nanotubes (SWCNTs), has been cross-linked by high pressure and high temperature (HP&HT) treatment at 513 K and pressures in the range 0.5 to 1.5 GPa to yield densified network polymer composites. A composite with 5 wt% SWCNTs showed 2.2 times higher tensile strength sigma(UTS) (sigma(UTS) = 17 MPa), 2.3 times higher Young's modulus E (E = 220 MPa) and longer extension at break than pure PI. The improvement is attributed to SWCNT reinforcement and improved SWCNT-PI interfacial contact as a result of the HP&HT cross-linking process, and reduced brittleness despite a higher measured cross-link density than that of pure PI. The latter may originate from an effect similar to crazing, i.e., bridging of microcracks by polymer fibrils. We surmise that the higher cross-link densities of the composites are due mainly to physical cross-links/constraints caused by the SWCNT-PI interaction, which also reflects the improved interfacial contact, and that the CNTs promote material flow by disrupting an otherwise chemically cross-linked network. We also deduce that the PI density increase at HP&HT cross-linking is augmented by the presence of CNTs.