Clustering algorithms can help reconstruct the assembly history of the Milky Way by identifying groups of stars sharing similar properties in a kinematical or chemical abundance space. However, although being promising tools, their efficiency has not yet been fully tested in a realistic cosmological framework. We investigate the effectiveness of the HDBSCAN clustering algorithm in the recovery of the progenitors of Milky Way-type galaxies, using several systems from the Auriga suite of simulations. We develop a methodology aimed at improving the efficiency of the algorithm and avoiding fragmentation: First, we use a 12-dimensional feature space including a range of chemodynamical properties and stellar ages; furthermore, we optimise the algorithm using information from the internal structure of the clusters of accreted stars. We show that our approach yields good results in terms of both purity and completeness of clusters for galaxies with different types of accretion histories. We also evaluate the decrease in efficiency due to contamination by in situ stars. While for accreted-only haloes the algorithm matches well the recovered clusters with the individual progenitors and is able to recover accretion events up to a redshift of accretion $z_{\rm acc}\sim3$, for accreted + in situ haloes it can only identify the more recent accretion events ($z_{\rm acc} < 1$). However, the purity of the identified clusters remains remarkably high even in this case. Our results suggest that HDBSCAN can efficiently identify accreted debris in Milky Way-type galaxies in realistic conditions, however, it requires careful optimization to provide valid results.