Global food prices are rising rapidly in response to a dramatic increase in global energy prices and the Ukraine-Russia war, causing severe impacts on the world’s poorest people. The FAO Food Price Index increased by 23% from May 2021 to May 2022 and the Cereals Price Index increased by 30%. Sanctions or blockades that restrict exports from Russia or Ukraine – two of the world’s most important food-exporting countries – are exacerbated by energy price rises which further increase food prices through higher costs for agricultural inputs, such as fertiliser. We consider the role of increasing agricultural input costs and the curtailment of exports from Russia and Ukraine to quantify the potential outcomes on human health and the environment. We show that the combination of agricultural inputs costs and food export restrictions could increase food costs by 60-100% in 2023 from 2021 levels, leading to the deaths of 400 thousand to 1 million additional people in 2023 and undernourishment of 60-110 million people. Furthermore, a reduction in land use intensification, arising from higher input costs, leads to agricultural land expansion, especially in the tropics, with potential consequences for deforestation and carbon and biodiversity loss. We find that the impact of agricultural input costs on food prices is larger than the effect of the curtailment of exports from Russia and Ukraine. Restoring food trade from Ukraine and Russia alone would be insufficient to substantially reduce the magnitude of the current food insecurity problem. We contend that the immediacy of the food export problems associated with the Ukraine-Russia war has diverted attention away from the principal causes of current global food insecurity, which may hinder the quest to find solutions.