H.E.S.S. Collaboration: et al. ; We report on the detection of very high energy (VHE; E > 100 GeV) γ-ray emission from the BL Lac objects KUV 00311−1938 and PKS 1440−389 with the High Energy Stereoscopic System (H.E.S.S.). H.E.S.S. observations were accompanied or preceded by multiwavelength observations with Fermi/LAT, XRT and UVOT onboard the Swift satellite, and ATOM. Based on an extrapolation of the Fermi/LAT spectrum towards the VHE γ-ray regime, we deduce a 95 per cent confidence level upper limit on the unknown redshift of KUV 00311−1938 of z < 0.98 and of PKS 1440−389 of z < 0.53. When combined with previous spectroscopy results, the redshift of KUV 00311−1938 is constrained to 0.51 ≤ z < 0.98 and of PKS 1440−389 to 0.14 ⪅ z < 0.53. ; The support of the Namibian authorities and of the University of Namibia in facilitating the construction and operation of H.E.S.S. is gratefully acknowledged, as is the support by the German Ministry for Education and Research (BMBF), the Max Planck Society, the German Research Foundation (DFG), the Helmholtz Association, the Alexander von Humboldt Foundation, the French Ministry of Higher Education, Research and Innovation, the Centre National de la Recherche Scientifique (CNRS/IN2P3 and CNRS/INSU), the Commissariat a l'Energie Atomique et aux Energies Alternatives (CEA), the U.K. Science and Technology Facilities Council (STFC), the Knut and Alice Wallenberg Foundation, the National Science Centre, Poland grant no. 2016/22/M/ST9/00382, the South African Department of Science and Technology and National Research Foundation, the University of Namibia, the National Commission on Research, Science and Technology of Namibia (NCRST), the Austrian Federal Ministry of Education, Science and Research and the Austrian Science Fund (FWF), the Australian Research Council (ARC), the Japan Society for the Promotion of Science, and the University of Amsterdam. We appreciate the excellent work of the technical support staff in Berlin, Zeuthen, Heidelberg, Palaiseau, Paris, Saclay, Tubingen, and in Namibia in the construction and operation of the equipment. This work benefited from services provided by the H.E.S.S. Virtual Organisation, supported by the national resource providers of the EGI Federation. The H.E.S.S. and Fermi/LAT analysis computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at Lunarc. Tomas Bylund and Yvonne Becherini wish to acknowledge the support of the Data Intensive Sciences and Applications (DISA) centre at Linnaeus University. Matteo Cerruti has received financial support through the Postdoctoral Junior Leader Fellowship Programme from “la Caixa” Foundation (LCF/BQ/PI18/11630012). This research made use of the NASA/IPAC Extragalactic Database (NED) and of the SIMBAD Astronomical Database, of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. We acknowledge the use of public data from the Swift data archive. This research made use of Gammapy, a community- developed core Python package for gamma-ray astronomy (Deil et al. 2017). This research has made use of data and software provided by the Fermi Science Support Center, managed by the HEASARC at the Goddard Space Flight Center. Part of this work is based on archival data, software or online services provided by the Space Science Data Center - ASI. This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France (doi:10.26093/cds/vizier). The original description of the VizieR service was published in A&AS 143, 23. This research has made use of the NASA/IPAC Infrared Science Archive, which is funded by the National Aeronautics and Space Administration and operated by the California Institute of Technology. ; Peer reviewed