Food prices could rise under a no-deal Brexit but supermarket shelves will not be bare, Dominic Raab has said.
The Foreign Secretary sought to play down grim warnings about price hikes and stockpiling as "bumps along the road" as post-Brexit trade talks were set to end on Sunday.
Boris Johnson and EU Commission chief Ursula von der Leyen agreed a decision would be made on whether a deal can be agreed at the weekend after a lengthy dinner in Brussels on Wednesday night.
The eleventh-hour meeting failed to reach a conclusion and raised fears the UK will be forced to trade on tariff-heavy World Trade Organisation terms next year - effectively a no-deal Brexit.
Britain's largest supermarkets are stockpiling food in case of no deal, with Tesco boss John Allan suggesting food bills could rise by up to 5% due to tariffs and disruption.
Ports like Dover, Felixstowe and Southampton could be hit with delays due to complex new border checks and a surge in imports.
Food and Drink Federation boss Ian Wright told MPs this week that "we can't be absolutely certain about the movement of food from EU to UK from January 1" due to border checks and tariffs.
Asked about price rises, Mr Raab told the BBC "I don't think that's a figure that we recognise" and tariffs would be a "very minor proportion" of food prices.
He said: "Of all the things that will be a challenge, I am not concerned about either supermarket cupboards running bare or the cost of food prices.
"Equally, there will be some bumps along the road if we don't get a free trade deal, that's the inevitable consequence of change.
"But we will be well braced and well prepared to deal with those, and we are going to make a success of leaving the transition period, come what may."
Mr Raab also failed to rule out Brexit talks continuing beyond the Sunday deadline.
He said the UK viewed the date as "a point we need some finality" but added: "You can never say never."
"If the EU moves substantially and actually we are only dotting a few Is and crossing a few Ts that's different," he told Sky News.
"But without movement on the crucial two, three areas I have described, I think that will be a point of finality and that is certainly the way the UK is approaching it."
It comes after Mr Allan, the Tesco chairman, said the supermarket giant was hoarding fresh food in case of a problems after January 1.
He said: “We are trying to ensure that we have stockpiled as much as we can of non-live product either in our own warehouses or with our suppliers.
“If we leave on a no-deal basis there will be tariffs, and those tariffs can be quite substantial on some food items.”
Mr Allan said there could be some shortages of fresh foods for a period of a month or two.
But he added: “I don’t think there is any reason at all for any consumer to panic or panic buy at the moment."
UK chief negotiator Lord Frost and his EU counterpart, Michel Barnier, will meet in Brussels on Thursday in a final push to salvage a deal.
