The adsorption of hydrogen on Au nanoparticles (NPs) of size of the order of 10 nm has been investigated by use of localised surface plasmon resonances (LSPR) in the NPs. The samples, formed by Au NPs obtained by oblique angle deposition on glass substrates, display a strong optical dichroism due to two different plasmon resonances dependent on the polarisation of light. This ensured the use of Transmittance Anisotropy Spectroscopy, a sensitive derivative optical technique, which permitted one to measure shifts of the LSPR as small as 0.02 nm upon H adsorption, which are not accessible by conventional plasmonic methods. The measured signal is proportional to the area of the NPs, which shows that H atoms diffuse on their facets. A negative charge transfer from Au to H is clearly demonstrated.