In this paper we present a novel algorithm for improved block-online supervised acoustic system identification in adverse noise scenarios by exploiting prior knowledge about the space of Room Impulse Responses (RIRs). The method is based on the assumption that the variability of the unknown RIRs is controlled by only few physical parameters, describing, e.g., source position movements, and thus is confined to a low-dimensional manifold which is modelled by a union of affine subspaces. The offsets and bases of the affine subspaces are learned in advance from training data by unsupervised clustering followed by Principal Component Analysis. We suggest to denoise the parameter update of any supervised adaptive filter by projecting it onto an optimal affine subspace which is selected based on a novel computationally efficient approximation of the associated evidence. The proposed method significantly improves the system identification performance of state-of-the-art algorithms in adverse noise scenarios.