Schools may have to close, exams could be disrupted and fresh food for pupils’ meals could run short because of panic buying with prices soaring by up to 20%, according to a secret Department for Education analysis of the risks of a no-deal Brexit obtained by the Observer.

The five-page document – marked “Official Sensitive” and with the instruction “Do Not Circulate” – also raises the possibility of teacher absences caused by travel disruption, citing schools in Kent as particularly at risk.

On the dangers of food shortages to schools, it suggests that informing the public of the risks could make matters even worse.

In a section entitled School Food, it talks of the “risk that communications in this area could spark undue alarm or panic food buying among the general public”.

And it adds: “Warehousing and stockpiling capacity will be more limited in the pre-Xmas period. The department has limited levers to address these risks. We are heavily dependent on the actions of major suppliers and other government departments to ensure continued provision.”

Listing the actions the department would take in the event of food shortages affecting schools, the document says: “In light of any food shortages or price increases we will communicate how schools can interpret the food menu standards flexibly. DfE may make exceptional payments – or submit a prepared bid to HM Treasury for additional funding. Worst case scenario estimate of the increased costs – £40 to £85m a year for schools in relation to free school meal provision based on price increases of 10-20%.”

The secret Department for Education analysis of the risks of a no-deal Brexit obtained by the Observer. Photograph: DfE

Under a heading School Travel, the analysis makes clear that the potential problems are “not countrywide”, and cites Dover in Kent as at the highest risk of disruption, stating: “Risk of travel disruption could result in school and early years settings closures, pupil and staff absence and exam disruption (though to a lesser extent in Oct due to limited exams being sat).”

Entitled “DfE No Deal Programme – Schools”, the document was drawn up by Lord Agnew, reappointed by Boris Johnson as parliamentary under-secretary for schools last week. It appears to have been written very recently as it refers to “short lead in time due to new PM” .

The leak was seized on last night by the Labour party. Shadow education secretary Angela Rayner called on Johnson to rule out a no-deal Brexit, which she said would pile more misery on a school system that had already suffered from years of Tory austerity cuts.

“This document lays bare the potential consequences of a disastrous no-deal Brexit for our schools and nurseries, and the parents and children who rely on them. By the government’s own admission, head teachers may be left unable to feed their pupils or forced to close their doors entirely.

“With our education system already at breaking point after years of Tory budget cuts, being forced to prepare for this kind of chaos is the last thing that schools and nurseries need. Boris Johnson must abandon his irresponsible and expensive obsession with no deal,” she said.

Angela Rayner, shadow secretary of state for education, says the chaos caused by no deal is the last thing schools need. Photograph: Martin Godwin/The Guardian

The analysis ranks the level of risks under a colour-coded system: green (where the department is confident the risks can be dealt with and delivery of services maintained as normal); amber (where delivery is “feasible but significant issues already exist requiring management attention”); and red (where delivery of normal services “appears to be undeliverable”).

The issues relating to school food and travel disruption that could lead to school closures and exam disruption are given amber warnings.

The document mentions a risk of shortages of medical supplies and equipment, particularly to special educational needs schools, but classifies the risk as green.

With Johnson insisting he will take the UK out of the EU “deal or no deal” on 31 October, the government announced plans last week to set aside an extra £2.1bn for no-deal preparations, including stockpiling of medicines, an extra 500 border officials and a public awareness campaign about possible disruption to travel and services. The prime minister is ramping up preparations for a no-deal Brexit, although he insists he still wants to leave the EU with a new agreement.

A DfE spokesperson said: “While we don’t comment on leaked documents, our … guidance to schools and other stakeholders already provides advice 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.”

Ian Watts, area education officer at Kent county council, said: “We have a duty to families to ensure schools do all they can to ensure provision, even in times of emergency.”

Other government documents obtained by Sky News last week warned of “consumer panic” and gaps in security within weeks of leaving the EU without a deal.