UK farmers will be encouraged to “grow more here” to prevent increases in food prices potentially caused by a no deal Brexit, a senior Cabinet minister has suggested.

Chris Grayling, the Transport Secretary, said he believed Britain and Brussels will be able to reach a “sensible agreement” on the UK’s terms of withdrawal from the European Union.

However, he insisted that the UK will “succeed come what may” as he sought to downplay concerns that leaving the bloc without a deal could lead to large increases in food prices.

He warned that no deal would cause “damage” to food producers on the continent but suggested the UK could counteract any problems by boosting domestic production in comments which echoed the famous “Dig for Victory” campaign of the Second World War.

Told that British families could be hit hard by rising food prices if new, post-Brexit trading arrangements are not put in place, Mr Grayling said: “Well, what we will do is grow more here and we’ll buy more from around the world.