Dover and other Channel ports face disruption of up to six months if the UK leaves the EU without a deal, ministers have said.
The revised warning comes after technical analysis by officials on traffic flows if there are delays with customs checks in a no-deal Brexit.
While this is regarded as a worst-case scenario, the public sector is being asked to rewrite its contingency plans.
NHS leaders are being urged to check plans medical supplies can be secured.
MPs will decide whether to back Theresa May’s Brexit deal in Parliament next Tuesday.
Downing Street is trying to rally support amid signs it is likely to be rejected by a large margin.
Updated advice to government departments from officials warns there could be six months of reduced access and delays at Dover and Folkestone if the UK leaves the EU on 29 March without a deal.
The BBC’s health editor Hugh Pym said departments are asking different parts of the public sector to check and if necessary rewrite their contingency plans.
This will include the NHS and a letter is being sent to health leaders today by the Secretary of State Matt Hancock telling them to check plans for ensuring medical supplies can be secured.
The existing message to the pharmaceutical industry will not be changed.
Current advice is that there should be a six-week stockpile of medicines in the UK to cover the possibility of disruption after a no deal Brexit.
About 90% of medicines imported by the UK and the Republic of Ireland come in through Dover.
Mr Hancock said the NHS should prepare to use alternative routes in the event of disruption on cross-channel routes, including the use of planes to fly in supplies.
Kent County Council has warned that dead bodies may remain uncollected and children might miss exams due to gridlocked roads in the event of a no-deal Brexit.
In an update on its contingency planning, the local authority said refuse could blight the streets and food deliveries could be disrupted as the county copes with 10,000 lorries parked or stacked on its roads.