Some of the claims made in relation to Brexit do seem to be exaggerated, particularly when one considers that we do not know what the final settlement will be (my best guess is that the EU and the UK will reach a deal and it will get through the House of Commons with the support of Labour dissidents).
However, this article suggests that higher fruit and vegetable prices could lead to a large number of early deaths: 5,600 deaths a year
Indeed, the article admits: 'Analysing the potential implications of Brexit is a tricky business. The concrete details of Brexit remain unclear. Proposals range from various forms of “soft Brexit” that include a new trade agreement with the EU, to a “hard Brexit” in which the UK falls back on the (higher) tariffs set out by the World Trade Organization.'
What is needed is for domestic policy to have a greater focus on growing fruit and vegetables, both for health reasons and to respond to the greater number of consumers who are vegetarians and vegans. That is lacking in current proposals.