Previous measurements in JET, as well as in other tokamaks, have found a minimum value of plasma density (ne), nth,min, below which the H-mode power threshold, Pthr , increases with decreasing ne. On the other hand, the multi-machine H-mode threshold scaling law, Pthr,08, is roughly linear with ne and the physics mechanisms underlying the 'roll-over' of Pthr at low ne are unexplained. It is of relevance to ITER, which foresees H-mode access at high BT (5.3T) and low ne, whether nth,min scales with BT and machine size. This paper reports on recent L-H threshold studies carried out in JET with the MkII-HD divertor at low density and two values of BT to provide additional input to these issues. Over the years, L-H threshold experiments at low ne in JET have shown similar Pthr in plasmas with either Neutral Beam (NB) or Ion Cyclotron Resonance Heating (ICRH). In ASDEX-Upgrade, similar Pthr has been reported for NBI and ECH heated plasmas over a wide range of ne. In JET, Pthr is not affected by variations in toroidal rotation due to TF ripple. On the other hand, in DIII-D Pthr is found to increase with injected torque and edge toroidal rotation in experiments that vary input power and torque independently by means of co- and ctr- NBI. New JET discharges with varying momentum input are analysed in this paper to investigate the influence of NB torque on Pthr. It is likely that the H-mode transition is linked to achieving critical edge conditions. The second part of this paper therefore focuses on the analysis of the edge parameters at the L-H transition, in order to provide input to the physics of edge transport barrier formation.