Previous work has shown that asymmetry in viral phylogenies may be indicative of heterogeneity in transmission, for example due to acute HIV infection or the presence of core groups with higher contact rates. Hence, evidence of asymmetry may provide clues to underlying population structure, even when direct information on, for example, stage of infection or contact rates, are missing. However, current tests of phylogenetic asymmetry (a) suffer from false positives when the tips of the phylogeny are sampled at different times and (b) only test for global asymmetry, and hence suffer from false negatives when asymmetry is localised to part of a phylogeny. We present a simple permutation-based approach for testing for asymmetry in a phylogeny, where we compare the observed phylogeny with random phylogenies with the same sampling and coalescence times, to reduce the false positive rate. We also demonstrate how profiles of measures of asymmetry calculated over a range of evolutionary times in the phylogeny can be used to identify local asymmetry. In combination with different metrics of asymmetry, this combined approach offers detailed insights of how phylogenies reconstructed from real viral datasets may deviate from the simplistic assumptions of commonly used coalescent and birth-death process models. 