The warning says the pharmaceutical industry needs that period of help from the government “to ensure adequate arrangements are in place to build stockpiles of medicines”.
It also says that it would take “at least 4-5 months” to make traders ready for the new border checks that might be required, including incentives to register for fresh schemes.
The note was revealed by The Financial Times as Mr Johnson – the overwhelming favourite to succeed Theresa May – launched his campaign on a pledge to leave the EU on 31 October “deal or no deal”.
It states that, while government departments had delivered around 85 per cent of their “core no-deal plans”, many of those provided only “a minimum viable level of capability”.
Prepared for a cabinet discussion on 21 May, it was never circulated because Ms May was concentrating at the time on her doomed attempt to force through her withdrawal agreement.
After that attempt collapsed, the prime minister announced her plans to resign – throwing the country into the uncertainty of the Tory leadership race.
Ed Davey, the Liberal Democrat home affairs spokesman, seized on the note, saying: “This lays bare the utter cynicism of Boris Johnson and his ilk.
“They are prepared to talk up crashing out of the EU to further their chances in the Tory leadership contest, despite government documents showing this would lead to shortages of medicines and chaos at our borders.”
Mr Johnson has drawn criticism for insisting the current Halloween night deadline must be met – regardless of whether he can strike a new deal with the EU.
At his launch, he said it was impossible to “unite this country” until “we have delivered on the primary request of the people; the one big thing they have asked us to do.”
He added: “After three years and two missed deadlines, we must leave the EU on October 31.”
Labour will lead a cross-party Commons move to block a no-deal exit on Wednesday, by seizing control of the Commons business to legislate later this month.
The confidential cabinet warning comes after Chris Grayling axed the notorious contracts for ferries to bring in emergency medicines – including with a firm with no ferries.
At Tuesday’s cabinet meeting, the transport secretary is reported to have warned that that how to bring in freight remained an urgent issue that had to be addressed.
The meeting was dominated by clashes over no-deal preparations, with some pro-Brexit ministers demanding huge extra sums be spent.
Sajid Javid, the home secretary and a leadership contender, called for up to £1.2bn extra to prepare Britain’s borders.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies