When Howard Hardiman, an artist who lives on a remote Scottish island, wrote on Twitter that he was stockpiling because he lives at the end of the supply chain, he drew abuse online from supporters of Britain’s departure from the bloc.

The government has repeatedly stated that there is no need for alarm, and that it expects to strike a deal soon with the European Union. An agreement would probably invoke a “standstill” transition period, during which few Britons would notice any changes until December 2020. The European Union says it, too, wants a deal, and it has made positive noises lately, though talks over the weekend failed to produce a breakthrough.

But even if the two sides reach an accord, it would still need approval from Parliament, where hard-line Brexit supporters in Mrs. May’s fractious Conservative Party are threatening to wreck any agreement because of her proposal to keep some close economic ties to the bloc. Instead, they want a much cleaner break, with some insisting that there is nothing to fear from a no-deal Brexit.

Analysts say that the possibility of disorderly rupture cannot be discounted — something that brings with it the risk of disruption to supplies and a decline in the value of the British currency, which would in turn drive up the costs of imported food and other goods (another reason to stockpile).

Ian Wright, the director general of the Food and Drink Federation, an industry group, said there was no sign so far of strains on supplies but predicted that stockpiling by consumers would start in earnest if there was no agreement on Brexit by next month. The supermarket chain Tesco has said it is discussing contingency plans to keep more dried goods.

For those reliant on imported medication, a disorderly Brexit is a particular worry, and the government has asked pharmaceutical companies to store six weeks’ supply of medication, though what would happen after that remains unclear. Supplies might be flown in, bypassing clogged ports, but experts say a no-deal exit could also interfere with air travel, grounding many flights from the European Union.