Panic buyers have cleared supermarket shelves of bottled water.
Tinned vegetables and toilet rolls are also running low as desperate shoppers stock up amid fears of biological or chemical terrorist attacks.
The items are on a list of recommended goods drawn up by the Home Office in case Britain comes under terrorist attack.
Although there is no specific terrorist threat, Home Office officials have said it is prudent to be prepared.
Asda's stores in Brighton Marina and Hollingbury and Tesco in Lewes had all sold out of water last night.
Other stores were expecting extra deliveries to prevent stocks drying up.
Last night, Nick King customer services manager at Asda Hollingbury, said: "We've been very busy and are completely out of bottled water.
"Some people are definitely panic buying, whereas others do not even seem to be aware of what is going on.
"We've still got a good stock of tinned foods but have noticed a rush on toilet rolls. We have been told by headquarters to expect more supplies of water very soon."
Allan Allbeury, 70, from Kemp Town, was among the shoppers who found the supermarket shelves bare at Tesco in Brighton Marina.
He said: "I just popped in to buy a single bottle of water and could not believe what I saw. There was not a drop left. People seem to be acting very irrationally."
Supplies of water were also low at Sainsbury's in The Drove, Newhaven.
The store was forced to put a new delivery of canned vegetables and bottled water on to the shelves as soon as it arrived last night, instead of waiting until this morning as usual.
Manager Jim Mullin said: "There were 8ft gaps in the shelves where the multi-packs of water once stood.
"People who perhaps would only buy one bottle of water have been buying packs of 12.
"There is no doubt people are panic buying. We have been told to expect bigger deliveries in the next few days."
Other stores were confident they had enough water, tinned food and toilet rolls to cope with demand.
Terry Smith, assistant manager at Iceland in Blatchington Road, Hove, said: "We have had a slight increase in sales but are certainly not worried we will sell out."
Simon Legg, deputy manager at Safeway in St James's Street, Brighton, said: "We almost sold out of bottled water for the first time yesterday.
"We have not seen panic buying on the same scale as when people are snowed in but it does seem as though people who would usually buy one bottle of water are now buying two or three."
Staff at Somerfield stores in Lancing and Burgess Hill and at Sainsbury's in Worthing admitted a surge of customers buying bottled water had left their stocks low.
Supermarkets in Eastbourne, hastings and St Leonards also reported panic buying of water, long life milk, tinned food and other non-perishables had left shelves bare.
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