Mr Bullock was countering suggestions that shoppers would feel the pinch when the UK leaves the EU.
He said: “As we get closer to leaving the EU, the more frequently dissident ‘remainers’ repeat their failed arguments from the referendum campaign.
“Paradoxically, although ‘Project Fear’ has been shown to be a nonsense, the more its protagonists return to it.
“We must reject their scare stories - there is no reason at all why Brexit should lead to higher food prices.
“Only 30 per cent of our food is imported from EU countries. In other words, 70 per cent of it, is not.
“Indeed, we should have every confidence prices will fall, as we are able to open up to new markets, and farmers globally realise they can trade with Britain without the EU’s Common External Tariff .
“Reports have shown Brexit could, for example, allow us to buy cheaper fruit and vegetables from Africa, with supermarkets looking to switch suppliers to those in both Africa and Asia. This would mean better prices for customers and boost ‘trade, not aid’ in a positive way.
“That food prices should fall after leaving the EU is not a wild prediction.
“Europhile Ted Heath expected food prices to rise 2.5 per cent each of the first six years Britain was in the EEC – why should they not fall when we leave?”
Mr Bullock also pointed to research from Warwick Lightfoot at the Policy Exchange which estimated food prices are 17 per cent higher in the EU, than they would be outside.
He concluded: “The poorer people are, the higher proportion of their income is spent on food. It is the lowest paid who have been hit in their shopping baskets by our membership of the EU.”