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The Times said the forecasts compiled by the Cabinet Office set out the most likely aftershocks of a no-deal Brexit rather than the worst case scenarios. Prime Minister Boris Johnson's office said it did not comment on leaked documents.
The newspaper said up to 85% of lorries using the main channel crossings "may not be ready" for French customs, meaning disruption at ports would potentially last up to three months before the flow of traffic improves.
The government also believes a hard border between the British province of Northern Ireland and the Republic of Ireland, an EU member, will be likely as current plans to avoid widespread checks will prove unsustainable, the Times said.
"Compiled this month by the Cabinet Office under the codename Operation Yellowhammer, the dossier offers a rare glimpse into the covert planning being carried out by the government to avert a catastrophic collapse in the nation's infrastructure," the Times reported.
"The file, marked "official-sensitive" — requiring security clearance on a "need to know" basis — is remarkable because it gives the most comprehensive assessment of the UK’s readiness for a no-deal Brexit."
Asked about the Yellowhammer documents, energy minister Kwasi Kwarteng told Sky News: "I think there's a lot of scaremongering around, and a lot of people are playing into 'Project Fear' ... We've got to prepare for no deal."
"We will be fully prepared to leave without a deal on the 31st of October."
The United Kingdom is heading towards a constitutional crisis at home and a showdown with the EU as Johnson has repeatedly vowed to leave the bloc on Oct. 31 without a deal unless it agrees to renegotiate the Brexit divorce.
After more than three years of Brexit dominating EU affairs, the bloc has repeatedly refused to reopen the Withdrawal Agreement which includes an Irish border insurance policy that Johnson's predecessor, Theresa May, agreed in November.
Though his move was largely procedural, in line with previously approved laws, Barclay said in a statement: "This is a clear signal to the people of this country that there is no turning back (from Brexit)."
A group of more than 100 lawmakers wrote to Johnson calling for an emergency recall of parliament to discuss the situation.
"We face a national emergency, and parliament must now be recalled in August and sit permanently until October 31 so that the voices of the people can be heard, and that there can be proper scrutiny of your government," the letter said.
Johnson will this week tell French President Emmanuel Macron and German Chancellor Angela Merkel that the Westminster parliament cannot stop Brexit and a new deal must be agreed if Britain is to avoid leaving the EU without one.
The prime minister is coming under pressure from politicians across the political spectrum to prevent a disorderly departure, with opposition leader Jeremy Corbyn vowing this week to bring down Johnson's government in early September to delay Brexit.
It is, however, unclear if lawmakers have the unity or power to use the British parliament to prevent a no-deal departure - likely to be the United Kingdom's most significant move since World War Two.
Opponents of no deal say it would be a disaster for what was once one of the West's most stable democracies. A disorderly divorce, they say, would hurt global growth, send shockwaves through financial markets and weaken London’s claim to be the world’s preeminent financial centre.
Brexit supporters say there may be short-term disruption from a no-deal exit but that the economy will thrive if cut free from what they cast as a doomed experiment in integration that has led to Europe falling behind China and the United States.