Kent County Council fears school meals could be compromised and migrant numbers could increase in the event of a "no-deal" Brexit.
Sky News has seen a report outlining the council's preparations for the UK leaving the EU without an agreement in place.
The document also warns:
:: 10,000 extra lorries would have to be "routinely" accommodated in Kent – creating traffic so bad that carers would be unable to reach patients, teachers would struggle to get to schools, and council staff would have to work from home
:: Waste collection could be delayed and disrupted
:: The administration of GCSEs and SATs could be compromised
:: The number of migrants arriving in Kent, including unaccompanied asylum-seeking children, could increase.
Kent Council has already spent more than £20m on reinforcing the region's roads, and has hired more staff to cope with Brexit-related disruption at a cost of hundreds of thousands of pounds.
Rob Bird, who leads the Liberal Democrat opposition of Kent County Council, said: "The people of Kent did not vote for disruption to food supplies. They did not vote to jeopardise care for society's most vulnerable or to risk our children's education. The threats of a no-deal Brexit are very real."
He also urged the county's MPs to insist that the government rules out the risk of a no-deal Brexit immediately.
Kent Council said the impacts of a "no-deal" scenario are dependent on further planning assumptions provided by the government and the future UK-EU relationship.
It said any long-term costs of any "new norm" arising from the change to border arrangements, such as infrastructure and staffing, will need to be identified.
The report notes that it is dependent on the government to provide appropriate funding in the situation of a no-deal Brexit, as well as further information and advice on issues including traffic disruption.
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Faisal Islam, Sky's political editor, said that a no-deal would be "a moment when the most efficient, forward-thinking, and prepared will make bets on the future, and the winners will take all".
He added that the government "simply do not want to believe that there will be any impact on anybody", and that the EU perceives that as no deal gets closer, its leverage increases, and the UK will be most impacted absolutely and relatively.
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