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Currently, external beam radiotherapy is faced with the challenge of delivering doses which exceed standard clinical fractions to target radioresistant tumours. However, any dose escalation in the tumour is limited by radiation tolerance of healthy tissues,including skin, which is among the most sensitive tissue. An improved efficiency can be accomplished at the cost of irreversible damage to these tissues. A similar problem is found when high doses are delivered to deep-seated tumours while trying to avoid intolerable doses in surrounding tissue. This thesis investigates a new treatment modality that uses a single Very High Energy Electron (VHEE, 50 - 250 MeV) beams focused by a magnetic lens to create a high dose region in a small volume, which is referred to here as a volumetric element. This can be scanned over the radioresistant regions of a tumour at typical depths of deep-seated cancers. Monte Carlo simulations were performed to model irradiation of a tissue-equivalent phantom with focused VHEE beams. These are confirmed by an experimental investigation of this treatment method that was undertaken at the CLEAR user facility at CERN. The results show a significant enhancement of the target dose and a simultaneous reduction of the dose to surrounding healthy tissue. The experimental part of this study required a new dosimetry protocol to be established for VHEEs. The energy dependence and dose response of radiochromic films up to 50 MeV were studied using the electron research accelerator at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig and the clinical accelerator at the National Physical Laboratory (NPL) in London. The response of radiochromic films in the VHEE range was cross-calibrated against alanine based secondary standard.