Who calls the shots on the bin collections in Sunderland, potholes in Hackney, or schools in Cardiff is not normally of interest to City traders in the multitrillion-pound sovereign bond market.

But for those dealing in UK government debt, Thursday’s local and devolved government elections are significantly more important than usual, amid speculation that a dire showing for Keir Starmer’s Labour party could topple him as prime minister.

“Usually local elections should not be a market relevant event, but this has indeed become one,” said Sanjay Raja, the chief UK economist at Deutsche Bank.

“Mainly as the repercussions, not just from a leadership challenge, but also any changes to fiscal policy and any pressure on fiscal rules the chancellor had signed up to. That is what the market is really signed up to.”

As the Iran war rattles the global economy, government borrowing costs have risen sharply worldwide. But in this sell-off, the UK has stood out, as investors dump the government’s bonds, known as gilts, more readily than the debts of its G7 peers.

The yield on 10-year UK government debt has risen by more than that in the US, France and Germany to trade above 5% – the highest level since the 2008 financial crisis – as investors demand a greater return for buying UK debt. On 30-year debt, the rate has climbed to the highest level since 1998.

Heaping pressure on the UK’s already stretched public finances, investors say Britain’s more significant exposure than its peers to the Middle East inflation shock, as a significant importer of energy, is the main driving factor. The Bank of England has said it could be forced to increase interest rates in response.

However, political risk and the prospect of a leadership challenge has also led some bond investors to rush for the exits.

Pollsters predict the loss of between 1,500 to 2,000 Labour local councillors across England, largely to Reform UK in the north and Midlands and the Greens in London. Control of the Welsh Senedd could be lost, alongside setbacks in the Scottish parliament.

James Smith, an economist at the Dutch bank ING, said: “Gilts are already under scrutiny due to inflation risks, and adding political uncertainty to the mix could further push [global] investors to look elsewhere.”

Underpinning the bond market anxiety are the Starmer’s potential successors, and a view they would shift Labour leftwards while increasing government borrowing.

Angela Rayner, the former deputy prime minister, is the bookmakers’ favourite, followed by Andy Burnham, despite the Greater Manchester mayor’s inability to run due to his lack of a parliamentary seat. Within cabinet there are also short odds on Ed Miliband, Wes Streeting and Shabana Mahmood.

Not all are viewed favourably in the Square Mile. Not least Burnham, after he argued last year that Britain was too “in hock to the bond markets”. His comments triggered a rise in yields in the £2tn market for UK government debt, but struck a chord with Labour voters frustrated by a lack of progress by Starmer and the chancellor, Rachel Reeves, amid tight-adherence to fiscal orthodoxy.

Burnham has since softened his stance in interviews with financial media outlets to explain his views.

One analyst said: “There’s been a realisation [in his camp] that there’s only so much talk you can give without being quite measured.”

Another said: “It’s the kind of statement you’d make as you try to vie for the leadership, but once you’re in, and understand the role of markets in funding government debt, it’s a different story. It was a message that would get toned down over time.”

That has not stopped the City betting that whoever replaces Starmer would lead a change that would probably require higher levels of public borrowing to finance.

“The starting point is there is a good deal of fear of a more leftwing agenda,” said Mark Dowding, the chief investment officer at the hedge fund RBC BlueBay.

“It’s tax and spend. The concern in the market is, look, the tax take is already at a historic high level, government spending is very elevated – you don’t have room to push further in that direction.”

But despite all the financial pressures and instability, many investors say that whoever replaces Starmer would have limited scope for a radical shift in fiscal policy.

“There is going to be inevitable discussion around the leadership. But I guess how much bad news is already baked into the cake?” said one City analyst.

“The view in the leveraged community is that even if you get a change of leadership, does much change in the UK? I think that is an important point to take away. What exactly might they do? They might not do very much.”

Avoiding bond market provocation has been central to Labour’s strategy under Starmer and Reeves. The party has doubled down on its pre-general election City charm offensive, while the chancellor has repeatedly pledged to maintain her “ironclad” fiscal rules, even as she stunned businesses with tax hikes such as the increase in employer national insurance contributions.

Much of the strategy behind her autumn budget was to coax gilt yields down to shrink Britain’s £100bn a year debt interest bill, representing £1 out of every £10 spent by the Treasury.

Almost a year ago, Reeves shedding a tear in the Commons, amid speculation she would be replaced, was enough to trigger a selloff in the gilt market. The incident arguably cemented her position, investors believe, with most viewing her as a bulwark against Labour increasing borrowing further.

Even as the US-Israeli war against Iran threatens to blow a multibillion-pound hole in the government finances, and with Labour under pressure to provide energy support and raise defence spending, Reeves has stuck to her rule. Burnham, in contrast, has said it could be bent to allow for more military spending.

In the City there is talk that any leadership contender could keep Reeves to smooth market concerns.

One analyst said: “She could become a linchpin for the market. [A new leader] could say: ‘Yes, we will do more and think about policy’, but keep her in place, as the fiscal credibility that comes with her and her rules are inviolate.”

However, such a view would underestimate two things: how deeply intertwined Starmer and Reeves’s fortunes have become, and the desire of British prime ministers to pick their own chancellor for reasons of allegiance and political signallin.

Dowding said Burnham, who also sparked a selloff when he unsuccessfully threw his hat in the ring for the Gorton and Denton byelection in January, would have a repair job on his hands if he wanted to be prime minister.

“If we were in a calm, benign market environment, maybe you could afford to disregard markets in such a way,” he said. “But if you look at the macro backdrop that we’re currently facing – looking at the deficit, and the rates of interest the UK is currently looking at – obviously we’re in a very strained position.

“The problem with his candidacy is that the gilt market would be very eager to take him at his word and test him out.”

Rayner has been beating a similar path to bond market credibility, wooing City investors in meetings held by the French investment bank BNP Paribas, as well as at an event last month to meet clients of the US-based lobbying firm Signum Global Advisors.

“I do know some clients found her reasonably persuasive, reasonably impressive, and a lot more reasonable than they otherwise would have thought,” said one analyst.

Four years ago, as Rishi Sunak battled Liz Truss for the Tory leadership, the then former chancellor sought to play on his City kudos, warning it would be “complacent and irresponsible” for his opponent to test bond market confidence.

Investors say the scars from what followed – a gilt market meltdown after Truss’s ill-fated mini-budget – remain fresh enough to linger over Britain’s fiscal credibility.

“Markets are much more cognisant of that kind of volatility [after Truss] and how it plays out. So there are a lot of watchful eyes as we go into the local elections at the potential worst outcomes for the leadership,” said Raja.

For any rivals to Starmer, this will be the challenge: changing direction without provoking a repeat episode.