At the Spitfire and Hurricane Memorial museum and cafe on the eastern tip of Kent, volunteers are preparing for an influx of new visitors if Britain crashes out of the European Union.

Manston airfield, visible from their windows and once the base for the aircraft that defended Britain during the second world war, is slated to be turned into a vast lorry park in a worst-case scenario where customs and border checks mean traffic backs up at ports.

For the last couple of weeks, locals say, they have watched diggers and heavy machinery at work, reinforcing the asphalt and laying out portable toilets and other services for thousands of trucks. “We’ll make a fortune off cups of tea,” jokes one museum volunteer.

The new lorry park is part of extensive preparations the county has drawn up, together with central government, to deal with the chaos that could ensue if Britain leaves without a deal in April.

Because of its location, Kent is expected to be on the frontline of any border problems. The former Brexit secretary Dominic Raab famously stunned critics with his admission that he “hadn’t quite understood the full extent” to which the UK was reliant on the crossing from Calais.

Dover handled 17% of the UK’s entire trade in goods in 2017, and that year more than 4 million lorries passed through the port or the Eurotunnel rail shuttle.

Schools have been warned to prepare for students stranded by traffic chaos if lorries start backing up. Kent police have been given an extra £3.5m to deal with the impact of Brexit. Kent Scientific Services has stockpiled six months’ worth of supplies for food and other safety tests, according to the latest Brexit planning. The council has also warned it could face “significant but as yet unquantified additional costs” from an unplanned exit.

A last-minute EU decision has now pushed back the date of a possible no-deal departure until mid-April but plans to stave off traffic chaos were so far advanced that the first measures are expected to go into effect anyway on Monday.

One side of the vital M20 motorway will be closed to normal traffic, with freight only heading towards the coast. The four London-bound lanes will be divided to carry passenger traffic both ways. Some lorries can be held on the motorway, if numbers build up, and when it fills up they will be redirected to Manston.

“It’s a joke, the roads can’t cope,” said Sally Chisholm, who works in a Royal British Legion care home on the coast near the area affected. “The traffic is already really bad round here.”

Sally Chisholm: “It’s a joke, the roads can’t cope.” Photograph: Emma Graham-Harrison/The Observer

Generally, though, Kent residents, who are used to problems in Dover spilling over into countywide gridlock, seem relatively sanguine about possible disruption from a no-deal exit.

They are much more anxious and frustrated about the state of Brexit itself, and the politicians handling it – regardless of whether they want to leave the EU or to remain.

“Nobody I’ve spoken to is worried [about impacts of no-deal],” said Pat Herrington, who lives just a few dozen metres from Manston and can see workers preparing it for lorries.

A single-issue voter, she opted for Leave because she believes Brexit is needed to end exports of live animals, still regularly shipped out of Ramsgate port. “For a lot of us, it is the only hope it would be stopped.”

Kevin Spooner, who has a stall at the market in Ramsgate, says he isn’t worried about the impact of no deal, because he is convinced that Brexit won’t happen. He voted Leave but has changed his mind and now wants a second referendum.

“Theresa May is getting three votes – why shouldn’t we have another one,” he says with a grin. “We’ve learned a lot more about the ins and outs of it [since the vote].”

Alan Brookes, headteacher of Fulston Manor school and chair of the Kent Association of Headteachers, said that although his school had made emergency plans for no deal, they were similar to ones in place for severe weather events such as blizzards. A greater headache for teachers, he said, was how the preoccupation with leaving Europe has eclipsed other issues, making it harder to focus on teaching at a time of austerity.

Melissa Pirbudak, 22, voted to leave but now regrets it. Photograph: Emma Graham-Harrison/The Observer

Most recently, the boiler has broken at his school, and if he doesn’t get emergency funds for the £80,000 cost of repairing it, Brookes may have to consider staffing cuts. But his requests for government aid have so far gone unanswered, he said.

“The major impact on the school is the fact that as long as Brexit drags on, there does not seem to be money for anything else.”

John Streeter, a former air-sea rescue pilot who volunteers at the Spitfire museum, says he has been waiting decades for Britain to leave the EU, since he first voted against joining in the 1970s, and would embrace a no-deal departure.

“I voted not to join originally,” he said. “I don’t really see what the point of a deal is.”

But, like many others in the area, he is now starting to wonder if it will happen at all. “I’d like to think that we can get out, but I don’t know one way or another.”

Melissa Pirbudak, 22, is equally frustrated by the political chaos but wants to see the opposite outcome. She voted Leave, but now wishes she had supported Remain, after a Brexit campaign she says was based on empty promises.

“They are waiting for us to leave; then [Brexit supporters think] some magical force field will cover England, and something wonderful will happen,” she said. “But no one knows what it is.