The five-page document, entitled “DfE No Deal Programme – Schools”, also says that schools may have to close and exams could be disrupted, if a no-deal Brexit goes ahead this autumn.
And it suggests that teachers might be absent from school, as a result of travel disruptions.
The document, marked “Official sensitive” and not intended for public circulation, was seen by the Observer newspaper.
In a section entitled “School food”, it says that panic-buying could result in a shortage of fresh food for pupils’ meals. But it suggests that informing the public of this might make the situation even worse.
It discusses the “risk that communications in this area could spark undue alarm or panic food-buying among the general public”.
The document adds: “Warehousing and stockpiling capacity will be more limited in the pre-Christmas period. The department has limited levers to address these risks.”
It offers a “worst-case scenario estimate of the increased costs – £40 to £85 million a year for schools, in relation to free school meal provision, based on price increases of 10 to 20 per cent”.
In a section headed “School travel”, the analysis says that risk of travel disruption in areas such as Kent “could result in school and early-years settings closures, pupil and staff absence and exam disruption (though to a lesser extent in October due to limited exams being sat)”.
The document was drawn up by Lord Agnew, who was reappointed by Boris Johnson as academies minister last week. Mr Johnson has said that he will take the UK out of the EU, “deal or no deal” on 31 October this year.
It also mentions a risk of shortages to medical supplies and equipment, particularly to special schools. But it classifies the risk here as relatively low, and the Department was confident that delivery of services would be maintained as normal.
A DfE spokesperson said: “While we don’t comment on leaked documents, our recently published guidance to schools and other stakeholders already provides advice and guidance on EU exit preparations for schools, including food provision, medical supplies and guidance for EU nationals.
“We are confident provision for schools will be protected in the event of the UK having to leave the EU without an agreement, and there are robust contingency plans in place to ensure schools are prepared in all eventualities.”