The stars in a globular cluster (GC) have always been considered coeval and of the same metallicity. Recently, this assumption has been challenged on the basis of spectroscopic and photometric observations, which show various generations of stars in GCs, differing in the abundances of products of H-burning at high temperatures. The main final product of this burning is He. It is then important to study the connections between stars properties and He content. We consider here the nearly 1400 stars on the red giant branch (RGB) observed with FLAMES@VLT in 19 Galactic Globular Clusters (GCs) in the course of our project on the Na-O anticorrelation. Stars with different He are expected to have different temperatures (i.e., different colours), slightly different metallicities [Fe/H], and different luminosity levels of the RGB bump. All these differences are small, but our study has the necessary precision, good statistics, and homogeneity to detect them. Besides considering the observed colours and the temperatures and metallicities determined in our survey, we computed suitable sets of stellar models - fully consistent with those present in the BaSTI archive - for various assumptions about the initial He content. We find that differences in observable quantities that can be attributed to variations in He content are generally detectable between stars of the primordial (P, first-generation) and extreme (E, second-generation) populations, but not between the primordial and intermediate ones (I). The only exception, where differences are also significant between P and I populations, is the cluster NGC 2808, where three populations are clearly separated also on the main sequence and possibly on the horizontal branch. The average enhancement in the He mass fraction Y between P and E stars is about 0.05-0.11, depending on the assumptions. The differences in Y, for NGC 2808 alone, are about 0.11-0.14 between P and I stars, and about 0.15-0.19 between P and E stars, again depending on the assumptions. When we consider the RGB bump luminosity of first and second-generation stars we find different levels; the implied Y difference is more difficult to quantify, but agrees with the other determinations.