This work investigates the formation mechanism of the turbulent secondary vortex street (SVS) which appears in the far wake of bluff bodies, when the (primary) Kármán vortex street is absent. The turbulent wakes of four types of highly porous bluff bodies (plates/meshes) are characterised via time-resolved particle image velocimetry and large eddy simulations. The effect of ambient turbulence and initial conditions on SVS development is also examined, by installing a turbulence grid upstream of the bodies, and by varying the homogeneity of the bluff body porosity. Our results indicate that the SVS is a far-wake evolution of near-wake shear-layer vortices which, in the absence of the vortex shedding instability, continually grow and are finally arranged into alternating vortices. Free-stream turbulence and body inhomogeneity are found to significantly influence SVS development by amplifying mixing and attenuating the shear-layer instabilities of the near wake, which in turn lead to the formation of weaker and less coherent SVS structures further downstream.