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Story by Dhara Ranasinghe and William Schomberg

By Dhara Ranasinghe and William Schomberg

LONDON (Reuters) -Britain's 30-year borrowing costs rose to their highest levels since 1998 and sterling slid more than 1% on Tuesday, highlighting growing investor anxiety about the UK's ability to get its finances under control.

The selloff in British government bonds, known as gilts, coincided with a broad selling across major bond markets where focus has again shifted on rising debt levels.

But the selloff in the pound, which was set for its biggest one-day fall since June 17, highlighted vulnerability in UK markets as concern about the ability of governments to exercise fiscal constraint grows.

"The UK has had a perilous (fiscal) backdrop and that's going to continue," said Lloyds FX strategist Nick Kennedy.

"Over the summer, there has been a bit of a risk premium built into the rates market. Investors are now wanting more of a risk premium for sterling as well."

Thirty-year gilt yields touched a peak of 5.69%, up five basis points on the day, their highest since May 1998.

Sterling was last down 1.2% on the day at $1.33 and almost 0.7% softer on the euro at 86.98 pence per euro.

When we're talking about the the 30 year bond yield,  UK borrowing costs hit 27-year high

It was by far the weakest performing G10 currency against the dollar.

CHALLENGES AHEAD

Finance minister Rachel Reeves is expected to raise taxes in her autumn budget in order to remain on course for her fiscal targets, potentially adding to the challenge of speeding up the economy.

And on Monday UK Prime Minister Keir Starmer reshaped his team, part of efforts to bolster his office before what is set to be a difficult end to the year.

"While a repricing of Bank of England expectations had helped sterling last month, the UK is going to be vunerable to fiscal risks as the Autumn budget approaches, which is likely to remain a headwind for sterling," said Jane Foley, head of FX strategy at Rabobank.

Britain is not the only country in the spotlight when it comes to fiscal worries.

France’s 30-year government bond yields surged to their highest levels in over 16 years on Tuesday, driven by fiscal concerns, as Prime Minister François Bayrou began talks with political parties in a bid to prevent a government collapse.

The latest selloff in bond markets came as Britain was selling a 10-year gilt via a syndicate of banks on Tuesday.

(Reporting by Dhara Ranasinghe, William Schomberg and Jaspreet Kalra ; Editing by Alun John and Karin Strohecker)