This paper reports H-mode plasma results from the 2009 JET He campaign which, as part of a wider ITPA study, have extended the physics basis to enable improved predictions of He, H-modes in ITER. L-H threshold experiments included the first ever dedicated study of the effect of concentration on the L-H threshold. He concentration, as measured by edge visible spectroscopy, was varied from 1 to 87% and was found to have little impact on the power threshold. This is in line with recent ASDEX Upgrade studies, but in contrast to JET 2001 results, which found that He plasmas have a 40% higher threshold than D equivalents. A study of the density dependence of the L-H threshold power in He and D found very different behaviour which may, in part, explain the differences between the JET 2001 and 2009 studies which were performed at different densities. The 2009 studies included the first experiment to measure the threshold required for Type I ELMs in He plasmas. A series of He and D plasmas with matched field (1.8T), current (1.7MA), shape (triangularity of 0.4) and divertor configuration were performed with different input powers. Similar Type I ELM power thresholds were found for the D (6.7-9.3MW) and He (7.5-9.3MW) plasmas. By normalising to a standard L-H threshold scaling, these results can be extrapolated to the ITER, He, half-field, baseline conditions (2.65T, 7.5MA and density of 85% of the Greenwald limit) where they predict a required input power of 42-48MW, or 23-86MW for an appropriately chosen 95% confidence interval. These intervals are largely consistent with the design auxiliary heating capacity of ITER. Confinement and ETB studies show that energy confinement times in He plasmas were approximately 60% of those for reference D ones, in line with previous studies on several machines. The relative impact of the core transport and ETB on this difference is assessed. IR camera measurements during He, Type I ELMs show that the heat load is deposited over significantly longer periods than for D equivalents. The impact of magnetic perturbations on Type I ELMs in He is also studied.