46 pages, 18 figures.-- ArXiv pre-print available at: http://arxiv.org/abs/0803.2039In this work we study the Lepton Flavour Violating semileptonic τ decays: 1) τ → μPP with PP = π+π−,π0π0,K+K−,K0{K[overline]}0; 2) τ → μP with P = π0,η,η' and 3) τ → μV with V = ρ0,Φ. We work within the context of two constrained MSSM scenarios: the CMSSM-seesaw and NUHM-seesaw, with a MSSM spectrum extended by three νR and their SUSY partners and where the seesaw mechanism for neutrino mass generation is implemented. A full SUSY one-loop computation is presented and the importance of the various contributions, the γ-, Z-, and Higgs bosons mediated ones, are analysed. The hadronisation of quark bilinears is performed within the chiral framework. Some discrepancies in the predicted rates for BR(τ → μη), BR(τ → μη') and BR(τ → μK+K−) are found with respect to previous estimates, which will be commented here. These three channels will be shown to be the most competitive ones to test simultaneously the Lepton Flavour Violation and the Higgs sector. We further present here a set of approximate formulas for all the semileptonic channels which we believe can be useful for further comparison with present and future data.This work has been supported in part by the EU MRTN-CT-2006-035482 (FLAVIAnet), by MEC (Spain) under grants FPA2006-05423 and FPA2007-60323, by Generalitat Valenciana under grant GVACOMP2007-156, by Comunidad de Madrid under HEPHACOS project and by the Spanish Consolider-Ingenio 2010 Programme CPAN (CSD2007-00042).Peer reviewed