It has been demonstrated that the difference between the Renormalised Brane World (RBW) model and the Lambda Cold Dark Matter ($\Lambda$CDM) model occurs only at sufficiently distant times. In this paper, it is shown that for spherically symmetric situations an analog deviation between the RBW model and Newton's theory occurs at large distances. More precisely, this deviation of the RBW model is nothing other than the explanation of Milgrom's hypothesis and follows from itself. Therefore, the results of this paper explains flat rotation curves of galaxies without dark matter.