10 pages, 4 figures. Accepted for publication in Astronomy & Astrophysics. (Abstract shortened)We observed the W28 field (for ~40 h) at Very High Energy (VHE) gamma-ray energies (E>0.1 TeV) with the H.E.S.S. Cherenkov telescopes. A reanalysis of EGRET E>100 MeV data was also undertaken. Results from the NANTEN 4m telescope Galactic plane survey and other CO observations have been used to study molecular clouds. We have discovered VHE gamma-ray emission (HESSJ1801-233) coincident with the northeastern boundary of W28, and a complex of sources (HESSJ1800-240A, B and C) ~0.5 deg south of W28, in the Galactic disc. The VHE differential photon spectra are well fit by pure power laws with indices Gamma~2.3 to 2.7. The NANTEN ^{12}CO(J=1-0) data r...