GRAPHIC-Why UK local elections matter for bond markets

* UK borrowing costs could rise further after local elections

* Gilt yields have risen the most among peers ​since Iran war

* Investors ⁠wary of a Starmer shift to the left, new leadership

LONDON, May ​6 (Reuters) - Britain's local elections on Thursday are in the spotlight for global bond investors, wary that a poor showing for the ruling Labour Party could pave the way to an unwelcome leadership challenge and renew ​concerns about ‌fiscal slippage.

Britain's borrowing costs remain the highest among rich economies and have risen the most since the Iran war, given its vulnerability to rising energy prices. Any further rise would add to the pressure ⁠on public finances.

Here are the key points for markets:

WHAT WILL INVESTORS WATCH?

Labour is widely expected ⁠to suffer sharp losses to the right-wing populist Reform and the ​left-wing Green Party in the elections for English local authorities and the Scottish and Welsh parliaments.

Investors will likely focus on the scale of the loss and whether it leads lawmakers to question Prime Minister Keir Starmer's future.

Expectations have risen that Starmer, who polls show has become deeply unpopular, will eventually be replaced.

Such speculation has risen after the scandal over his appointment of Peter ​Mandelson as U.S. ambassador, ‌sacked last September after a trove of emails revealed the depth of Mandelson's ties with the late convicted U.S. sex offender Jeffrey Epstein.

Odds on betting platform Polymarket show less than a 10% chance of an immediate Starmer departure, but it rises to almost 70% by year-end.

HOW WILL BOND MARKETS REACT?

That depends on the scale of Labour's loss.

A lot of bad news is priced into gilts, so a significant selloff after the vote would require a "catastrophic" result, said Royal London Asset Management's head of rates and cash Craig Inches.

A better-than-expected result ​for Labour could prompt a relief rally, said Inches, who is positioned for falling gilt yields.

WHAT IS THE RISK LONGER TERM?

A further rise in yields, particularly longer-dated ones.

Inflation fears since ‌the start of the Iran war have already helped send benchmark 10-year yields up some 70 basis points to 4.95%.

Britain's 30-year yields touched their highest since 1998 earlier this week.

Investors are worried Starmer will be pressured to shift policy to the left ‌or will eventually be replaced by a more left-wing leader who could push for more spending.

Colin Finlayson, fund manager at Aegon Asset Management, said almost anyone replacing Starmer would be less favourable to markets, while Starmer shifting left would also mean less fiscal discipline.

Gilt yields would also rise on signs that finance minister Rachel Reeves, whose commitment to fiscal rules ​limiting borrowing has reassured investors, might be replaced, said Finlayson, who is underweight gilts.

Turning to potential leadership candidates, investors said the gilt market would react negatively to former Deputy Prime Minister Angela Rayner and Manchester mayor ‌Andy Burnham, seen by some media commentators as possible successors to Starmer. Health secretary Wes Streeting is regarded as less of a threat.

Burnham said last year Britain needed to move beyond "being in hock to the bond markets", irking investors.

There is a case to consider defence spending outside the fiscal rules, Burnham told Bloomberg last week, adding the rules will stay but should ⁠not stand ⁠in the way of defence spending.

Burnham would however need to take up a parliamentary seat to trigger a leadership contest, ‌while Rayner remains under investigation for her tax affairs.

Politics will keep UK bonds volatile but 10-year yields above 5.25% would be a buying opportunity, said Franklin Templeton's head of European fixed income David Zahn.

HOW DOES THE ​IRAN WAR COMPLICATE THINGS?

The surge in bond yields ​and anticipated growth slowdown are challenging Britain's public finances for sure.

Deutsche Bank estimates the margin Reeves has to meet ‌her fiscal rules limiting borrowing has already shrunk to around 10 billion pounds ($13.62 billion), from nearly 24 billion in April, suggesting another challenging budget in the autumn.

Rising bond yields and traders' sharp shift from betting on rate cuts to rate hikes have left the gilt market more fragile. Still, some big investors have seen the war-driven rise in yields as a buying opportunity.