Recent results from the HESS gamma ray telescope have shown the presence of both a diffuse, extended, flux of gamma rays above 0.4 TeV and discrete sources in and near the Galactic Centre. Here, we put forward a possible explanation in terms of the diffusion of cosmic ray protons from a succession of supernova remnants ( SNR ) in the SgrA* region of the Galaxy plus a contribution from SNR in the rest of the Galactic Centre Region, to be called the Galactic Centre Ridge ( GCR ). Protons are favoured over electrons because the mG magnetic fields in the Region will attenuate energetic electrons = severely. Prominent features are the need for 'anomalous diffusion' of the protons in the whole region and the adoption of low efficiency for SNR acceleration in the high density regions. The latter is related by us to the well-known low 'cosmic ray gradient' in the Galaxy. A corroborating feature is the close correlation of inferred cosmic ray intensity with the smoothed intensity of 5 GHz radio radiation. We attribute this to the presence of the SNR in the GCR.