The environmental evaluation of food waste prevention is considered a challenging task due to the globalised nature of the food supply chain and the limitations of existing evaluation tools. The most significant of these is the rebound effect: the associated environmental burdens of substitutive consumption that arises as a result of economic savings made from food waste prevention. This study introduces a holistic approach to addressing these challenges, with a focus on greenhouse gas (GHG) emissions from household food waste in the UK. It uses a hybrid life-cycle assessment model coupled with a highly detailed multi-regional environmentally extended input output analysis to capture environmental impacts across the global food supply chain. The study also takes into consideration the rebound effect, which was modelled using a linear specification of an almost ideal demand system. The study finds that food waste prevention could lead to substantial reductions in GHG emissions in the order of 706-896 kg CO$2$-eq. per tonne of food waste, with most of these savings (78%) occurring as a result of avoided food production overseas. The rebound effect may however reduce such GHG savings by up to 60%. These findings provide a deeper insight into our understanding of the environmental impacts of food waste prevention: the study demonstrates the need to adopt a holistic approach when developing food waste prevention policies in order to mitigate the rebound effect and highlight the importance of increasing efficiency across the global food supply chain, particularly in developing countries.