Recently, the ideas of topological photonics were extended to a wide class of bianisotropic electromagnetic continua with a spatial cut-off in the material response [Phys. Rev. B, 92, 125153, 2015]. Importantly, conventional material models, for example the permittivity response of a magnetized plasma, are local and hence these materials do not fall precisely into the class of media that can be topologically classified. Here, it is shown that these seemingly limitations of topological photonics in a continuum can enable a giant field concentration and ultra-singularities of the electromagnetic field in a hotspot.