The K- and Co-doped BaFe2As2 (Ba-122) superconducting compounds are potentially useful for applications because they have upper critical fields (H-c2) of well over 50 T, H-c2 anisotropy gamma < 2 and thin-film critical current densities J(c) exceeding 1MA cm(-2) (refs 1-4) at 4.2 K. However, thin-film bicrystals of Co-doped Ba-122 clearly exhibit weak link behaviour for [001] tilt misorientations of more than about 5 degrees, suggesting that textured substrates would be needed for applications, as in the cuprates(5,6). Here we present a contrary and very much more positive result in which untextured polycrystalline (Ba0.6K0.4)Fe2As2 bulks and round wires with high grain boundary density have transport critical current densities well over 0.1MA cm(-2) (self-field, 4.2 K), more than 10 times higher than that of any other round untextured ferropnictide wire and 4-5 times higher than the best textured flat wire(7). The enhanced grain connectivity is ascribed to their much improved phase purity and to the enhanced vortex stiffness of this low-anisotropy compound (gamma similar to 1-2) when compared with YBa2Cu3O7-x (gamma similar to 5).