Two-dimensional (2D) perovskites with the general formula APbX are attracting increasing interest as solution processable, white-light emissive materials. Recent studies have shown that their broadband emission is related to the formation of intra-gap colour centres. Here, we provide an in-depth description of the charge localization sites underlying the generation of such radiative centres and their corresponding decay dynamics, highlighting the formation of small polarons trapped within their lattice distortion field. Using a combination of spectroscopic techniques and first-principles calculations to study the white-light emitting 2D perovskites (EDBE)PbCl and (EDBE)PbBr, we infer the formation of Pb , Pb, and X (where X = Cl or Br) species confined within the inorganic perovskite framework. Due to strong Coulombic interactions, these species retain their original excitonic character and form self-trapped polaron-excitons acting as radiative colour centres. These findings are expected to be relevant for a broad class of white-light emitting perovskites with large polaron relaxation energy.