The discovery of superconductivity at 39 K in magnesium diboride, MgB2, raises many issues, a critical one being whether this material resembles a high-temperature copper oxide superconductor or a low-temperature metallic superconductor in terms of its behaviour in strong magnetic fields. Although the copper oxides exhibit very high transition temperatures, their in-field performance is compromized by their large anisotropy, the result of which is to restrict high bulk current densities to a region much less than the full magnetic-field-temperature (H-T) space over which superconductivity is found. Moreover, the weak coupling across grain boundaries makes transport current densities in untextured polycrystalline samples low and strongly sensitive to magnetic field. Here we report that, despite the multiphase, untextured, microscale, subdivided nature of our MgB2 samples, supercurrents flow throughout the material without exhibiting strong sensitivity to weak magnetic fields. Our combined magnetization, magneto-optical, microscopy and X-ray investigations show that the supercurrent density is mostly determined by flux pinning, rather than by the grain boundary connectivity. Our results therefore suggest that this new superconductor class is not compromized by weak-link problems, a conclusion of significance for practical applications if higher temperature analogues of this compound can be discovered.