Body wave observations of the Earth's inner core show that it contains strong seismic heterogeneity, both laterally and radially. Models of inner core structure generated using body wave data are often limited by their parameterisation. Thus, it is difficult to determine whether features such as anisotropic hemispheres or an innermost inner core truly exist with their simple shapes, or result only from the chosen parameterisation and are in fact more complex features. To overcome this limitation, we conduct seismic tomography using transdimensional Markov Chain Monte Carlo on a high quality dataset of 5296 differential and 2344 absolute P-wave travel times. In a transdimensional approach, the data defines the model space parameterisation, providing us with both the mean value of each model parameter and its probability distribution, allowing us to identify well versus poorly constrained regions. We robustly recover many first order observations found in previous studies without the imposition of a priori fixed geometry including an isotropic top layer (with anisotropy less than 1%) which is between 60 and 170 km thick, and separated into hemispheres with a slow west and a faster east. Strong anisotropy (with a maximum of 7.2%) is found mainly in the west, with much weaker anisotropy in the east. We observe for the first time that the western anisotropic zone is largely confined to the northern hemisphere, a property which would not be recognised in models assuming a simple hemispherical parameterisation. We further find that the inner most inner core, in which the slowest anisotropic velocity direction is tilted relative to Earth's axis of rotation (), is offset by 400 km from the centre of the inner core and is restricted to the eastern hemisphere. We propose that this anomalous anisotropy might indicate the presence of a different phase of iron (either bcc or fcc) compared to the rest of the inner core (hcp).