Ministers have repeatedly played down the risk of shortages in the event of a sudden hard Brexit next March.
There are fears a no deal Brexit could stop imports of food and other supplies, such as medicine, to Britain.
Last week Brexit secretary Dominic Raab insisted there would be adequate food supplies.
Asked whether the Government was considering stockpiling food to cope with a "no deal" Brexit, Raab said: "It would be wrong to describe it as the Government doing stockpiling.
"What we will make sure - and of course the idea that we only get food imports into this country from one continent is not appropriate - but we will look at this issue in the round and make sure that there is adequate food supply."
In an interview with 5 News on Wednesday, Prime Minister Theresa May did not deny stockpiling is happening.
But she insisted the Government is being "responsible and sensible" while still trying to get a good deal with the European Union.
May said: "Far from being worried about preparations that we are making, I would say that people should take reassurance and comfort from the fact that the Government is saying we are in a negotiation, we are working for a good deal - I believe we can get a good deal - but... because we don't know what the outcome is going to be... let's prepare for every eventuality."
Supermarkets are asking suppliers to start planning for 'no deal'
Supermarkets have started asking suppliers to begin planning for a "no deal" Brexit.
Fears have been mounting the UK is set to crash out of the EU in March, with concerns for supplies of food and medicine.
German supermarket Aldi has now emailed suppliers saying it wanted to work with them "to help understand the potential implications", according to The Sunday Times
A spreadsheet was attached to the email showing a breakdown of ingredients and packaging materials, that are all sourced for the EU.
A supplier of coffee to Aldi, Giles Hurley, said he was thinking of storing six to eight weeks stock.
He said: "Most of the major retailers have been asking their suppliers how are planning for the implications of Brexit- and especially how we are planning to ensure we do not out of the goods we bring in from the EU.
"They can easily sit back and say they have no plans or concerns because, as usual in this relationship, it will be the suppliers who make the plans."
But one chairman of a big grocer said "we're some way off no deal and tariffs being imposed and queues at Dover".
