The one dimensional transport code RITM was previously applied to simulate self-consistently the radial profiles of plasma parameters in the L-mode of confinement in several tokamaks. In order to describe both the L-H transition and the H-mode itself a model for Drift Alfven (DA) instability, which predicts strong reduction of DA anomalous transport at high pressure and low collisionality, has been incorporated into RITM. Additionally to the suppression of DA turbulence H-mode conditions require also that Ion Temperature Gradient (ITG) modes, which control anomalous transport in the plasma core, should be damped in the edge transport barrier. It is demonstrated that the radial density gradient, being very sharp at the plasma edge due to ionisation of recycling neutrals, plays a crucial role in damping of ITG transport in the barrier, crucially supplementing the effect of radial electric field. The results of modelling of L-H transition in JET, when the heating power exceeds a critical level, and of confinement degradation under a too strong puffing of impurities, are presented. The capability of the code RITM to reproduce the experimental scalings for the radial width of the edge pedestal is demonstrated.