It has been pointed out that supersymmetric extensions of the Standard Model can induce significant changes to the theoretical prediction of the ratio Γ (K → eν)/Γ (K → μν) ≡ RK , through lepton flavour violating couplings. In this work we carry out a full computation of all one-loop corrections to the relevant ν H+ vertex, and discuss the new contributions to RK arising in the context of different constrained (minimal supergravity-inspired) models which succeed in accounting for neutrino data, further considering the possibility of accommodating a nearfuture observation of a μ → eγ transition. We also reevaluate the prospects for RK in the framework of unconstrained supersymmetric models. In all cases, we address the question of whether it is possible to saturate the current experimental sensitivity on RK while in agreement with the recent limits on B-meson decay observables (in particular BR(Bs → μ+μ−) and BR(Bu → τν)), as well as BR(τ → eγ ) and available collider constraints. Our findings reveal that in view of the recent bounds, and even when enhanced by effective sources of flavour violation in the righthanded ẽ − τ̃ sector, constrained supersymmetric (seesaw) models typically provide excessively small contributions to RK . Larger contributions can be found in more general settings, where the charged Higgs mass can be effectively lowered, and even further enhanced in the unconstrained MSSM. However, our analysis clearly shows that even in this last case SUSY contributions to RK are still unable to saturate the current experimental bounds on this observable, especially due to a strong tension with the Bu → τν bound.