The required heating power, P-LH, to access the high confinement regime (H-mode) in tritium containing plasmas is investigated in JET with ITER-like wall at a toroidal magnetic field of B-t = 1.8 T and a plasma current of I-p = 1.7 MA. PLH, also referred to as the L-H power threshold, is determined in plasmas of pure tritium as well as mixtures of hydrogen with tritium (H-T) and mixtures of deuterium with tritium (D-T), and is compared to the L-H power threshold in plasmas of pure hydrogen and pure deuterium. It is found that, for otherwise constant parameters, P-LH is not the same in plasmas with the same effective isotope mass, A(eff), when they differ in their isotope composition. Thus, A(eff) is not sufficient to describe the isotope effect of P-LH in a consistent manner for all considered isotopes and isotope mixtures. The electron temperature profiles measured at the L-H transition in the outer half of the radius are very similar for all isotopes and isotope mixtures, despite the fact that the L-H power threshold varies by a factor of about six. This finding, together with the observation of an offset linear relation between the L-H power threshold, P-LH, and an effective heat diffusivity, ?(eff), indicates that the composition-dependent heat transport in the low confinement mode (L-mode) determines, how much power is needed to reach the necessary electron temperatures at the edge, and hence P-LH.