Long-term UK borrowing costs soared to the highest level in almost three decades on Tuesday amid fears about a change of Labour leadership, before dropping back as cabinet ministers rallied around Keir Starmer.

With investors worried about potential changes to Labour’s tax and spending plans, the yield – in effect the interest rate – on 30-year government bonds jumped 11 basis points on Tuesday morning to 5.794%, the highest since May 1998.

Yields later fell back slightly, after the prime minister told a cabinet meeting on Tuesday morning that he would not resign and that the process for a leadership challenge had not been triggered. Shortly 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 Starmer to quit.

Starmer 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.”

After the cabinet meeting, several cabinet ministers including Peter Kyle, the business secretary, Liz Kendall, the technology secretary, and the housing secretary, Steve Reed, told reporters they were supporting Starmer.

Starmer’s comments and their support appeared to bring some calm to jittery financial markets. The benchmark 10-year yield on UK government bonds dropped back to below 5.1%, having hit 5.13% earlier in the day, while the 30-year yield dropped to 5.76%, after touching a new 28-year high of 5.81%.

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

Higher yields, if sustained, can raise the cost of borrowing for the government, consumers and businesses. Yields on the bonds of most major economies have been rising this year because of the inflationary impact of the Middle East conflict – but the UK has been hit especially hard.

Investors are weighing the potential impact of a change of leadership – or a lengthy period of internal Labour unrest. Two potential frontrunners to succeed Starmer, Angela Rayner and Andy Burnham, have hinted they would like to see higher public spending.

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.”

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.”