In the port of Whitehaven, a homemade banner affixed to an industrial garage confronts those arriving by train: “Save services at West Cumberland Hospital. Do not arrive D.o.A at Carlisle.”

The local hospital risks losing its major trauma and maternity units – with ambulances facing a 40-mile journey in unpredictable rural traffic. Just about every shop window in Whitehaven and beyond bears a poster urging action.

For the Labour party, which trails dismally in national polls, a row involving the crisis-torn NHS should be a gift, especially before a crucial byelection in the area. But right now the party cannot buy a break. The sprawling Copeland constituency, in which Whitehaven sits, is part of Britain’s self-styled “energy coast” – home to Sellafield and the proposed site of Europe’s largest nuclear power plant at Moorside. Nuclear energy is the area’s major employer and, as the Conservative party have been quick to underline, Labour’s leader Jeremy Corbyn is no fan of nuclear power.

The nuclear question could be crucial in determining a contest that Labour can scarcely afford to lose. The byelection, for which no date has yet been set, has been prompted by the resignation of local MP Jamie Reed, who has gone to work for Sellafield. The loss of a formerly safe Labour seat would deepen fears that – after being all but wiped off the map in Scotland – the party is on the verge of some kind of implosion in the north of England.

Copeland has already shunned Labour once, ignoring the party line and voting to leave the EU by a margin of 62%. The Tories, who squeezed Labour’s majority to just 2,564 in 2015, have not held this seat since 1935; a victory in Copeland would make them the first government to make a byelection gain since 1982.

As well as the NHS, Labour also hopes to fight on local issues such as Copeland’s woeful road and rail infrastructure – the 40-mile journey to Carlisle takes an hour and 10 minutes in two-carriage diesel trains – and the impact of austerity on public services. But Tory mailshots to thousands of homes already warn of threats to jobs at Sellafield while Ukip will appeal to local concerns on immigration.

Facebook Twitter Pinterest Labour’s Jamie Reed, whose resignation triggered the byelection. Photograph: Gary Calton/The Observer

Copeland’s mayor, plain-speaking independent Mike Starkie, says the area is in desperate need of fresh thinking from central government – and that a new approach to immigration that prioritises skilled workers could be the answer.

“The general perception here would be that people in Westminster don’t care about places like this,” said Starkie, who voted for Brexit. “We’ve got to be able to attract bright people from all over. Somebody from Poland shouldn’t get an advantage over a better-qualified Brazilian just because they’re from Poland. Immigration is good for any country. But first and foremost we’ve got to think of this area’s needs. If you could find me 200 specialist consultants who could go into the hospital tomorrow, the whole community would welcome them with open arms. But we need professional people.”

The nuclear industry in Copeland employs 10,000 people directly and supports thousands more jobs in the supply chain. “If Sellafield shut tomorrow – which it can’t – we might as well lock the gates on the town,” says Starkie.

Labour must convince locals that their leader doesn’t want this to happen. The problem, says Whitehaven councillor Christine Wharrier, is that “people assume Corbyn is anti-nuclear everything. There is a distrust there. They know he’s anti-nuclear weapons, so regardless of what he says about nuclear power – and he never has said he’s anti-nuclear power – it’s easy for the Tories.”

“Employment at Sellafield is not at risk in any way whatsoever – it’s a decommissioning plant and those jobs will be secure for half a century,” she said. “But the Tories are playing to people’s fears. We saw the same with Brexit. People want to look after themselves and their families – and that means they’ll sometimes accept myths as fact.”

Other Labour campaigners echo her concerns. “You’d be hard-pressed to find an elected Labour person in Copeland who doesn’t have a link to the nuclear industry,” said Whitehaven councillor Bill Kirkbride. “We’d have no economy otherwise. But the general view on the doorstep regarding the leader is an issue without a doubt. If they bring up the issue of Jeremy’s attitude to nuclear, we have to tell them he doesn’t write party policy. He’s entitled to his private thoughts like any MP and councillor.”

Down the coast in Seascale – the windswept village that is home to Sellafield – Corbyn looms large in Tory councillor David Moore’s sights. “Labour will campaign on the NHS because they’re desperate to stay away from nuclear. Jamie Reed resigned from the shadow cabinet on the grounds of nuclear when he was elected first time around. So even the current Labour MP doesn’t trust Corbyn on nuclear. Why should local people?”

The early favourite for the Labour candidacy, charity worker Rachel Holliday, whose candidacy was announced last Friday, has moved quickly to try to to defuse the issue. “The West Cumbrian men and women in our nuclear industry should be considered heroes,” she said. “While, as a mum, I ultimately want my kids to live in a world without nuclear weapons, it’s vital we protect the tens and thousands of high-skilled jobs, livelihoods and communities that are reliant on it.”

Back in Whitehaven, Starkie – who says the campaign should not be fought on single issues – says a Tory win could precipitate an early general election and the beginning of the end for Corbyn. He was not surprised by Reed’s departure. The outgoing MP’s young children, six-hour commute and well-documented antipathy to Corbyn, combined with imminent boundary changes (Cumbria will lose one of its six MPs) meant it was a case of when, not if. His party now faces a fight for its life in a seat that, until recently, it would have never expected to lose.

“I don’t think people feel betrayed by Jamie – he was a popular, local lad,” said one councillor. “But it has left a gap. It has left a gap that we could’ve done without.”