Long-term UK borrowing costs have soared to the highest level in nearly three decades while the pound and stocks fell as investors braced for a potential change of leadership, with cabinet ministers urging Keir Starmer to quit.

With investors worried about potential changes to the fiscal rigour of Starmer’s government, the yield – in effect the interest rate – on 30-year government bonds jumped 11 basis points to 5.794%, the highest since May 1998.

Starmer told a cabinet meeting on Tuesday morning that he would not resign and that the process for a leadership challenge had not been triggered. Immediately before the meeting, Miatta Fahnbulleh became the first minister to resign since Labour’s significant losses at last week’s local and devolved elections, calling on him to quit.

He said: “The Labour party has a process for challenging a leader and that has not been triggered. The country expects us to get on with governing. That is what I am doing and what we must do as a cabinet.”

His comments appeared to fail to calm jittery financial markets. The benchmark 10-year yield on UK government bonds (known as gilts) also rose 12 basis points to 5.12%, just below the highest levels since 2008 that it hit in March amid fears that the Iran war would stoke inflation.

The pound dropped 0.6% to $1.353 and was 0.3% lower against the euro at 86.8p a euro.

Neil Wilson, an investor strategist at Saxo Markets, said: “We could see a blowout in longer-dated gilts if this turns into a dogfight – political, fiscal and inflationary risks will rise. Markets tend to dislike a lack of certainty over who runs a government; the fiscal position is already fragile and likely to become worse should a left-leaning ticket prioritise spending, and that makes inflation stickier.”

Investors are concerned that if Starmer is forced out of Downing Street, his possible replacements may seek to increase public spending and loosen the government’s fiscal rules. Two potential frontrunners to succeed him, Angela Rayner and Andy Burnham, have hinted they would like to see higher public spending.

Mohit Kumar, the chief economist for Europe at Jefferies, said: “A managed exit would be our base-case scenario. Any replacement would likely be left leaning and be negative for the long end of the curve and the currency.” He said he expected a widening between shorter- and longer-dated UK borrowing costs, and was betting against the pound.

Stocks were also under pressure, with the FTSE 100 index down nearly 1%. Bank shares fell, with Barclays dropping 4% in early trade, while NatWest and Lloyds slipped more than 3%.

Gilt yields had already risen this week amid concerns over a jump in energy prices leading to higher inflation. Oil prices rose nearly 1% on Tuesday as talks to end the US-Israel war on Iran appeared fragile. Brent crude futures rose 2.7% to $106 a barrel, while US West Texas Intermediate gained 99 cents, or 1%, to $99.06 a barrel.

Donald Trump said on Monday the ceasefire with Iran was “on life support”, pointing to disagreements over several demands such as the cessation of hostilities on all fronts, the removal of a US naval blockade, the resumption of Iranian oil sales and compensation for war damage.

Tehran stressed its sovereignty over the strait of Hormuz, through which about a fifth of global oil and liquefied natural gas flows in normal times, and where hundreds of tankers and cargo ships remain trapped.

Suvro Sarkar, who leads the energy team at Australia’s DBS Bank, said: “Optimism regarding an imminent [peace] deal seems to be fading again and if we don’t see a deal by the end of May then upside risks for oil prices are definitely on the table.”

Kathleen Brooks, the research director at XTB, said: “There is an upward bias for bond yields anyway, and the UK yields are facing a double whammy of an energy price spike and a political crisis. The risk is that we get a bond market meltdown in the UK in the coming days.

“If that happens, will it quiet the factions of the Labour party who have threatened to ignore the bond market, ditch fiscal rules and boost public spending even more? Right now, it’s hard to see how the bond market can stabilise, and there could be further downside ahead.”