Kathleen Brooks, research director at XTB, said the falls meant the pound was 1.5% lower this week.
“This is a sign that Burnham is the least market-friendly of all the candidates, as Wes Streeting’s resignation did not have the same negative effect on the pound,” she said.
Over the past week 10-year yields have surpassed levels last reached in 2008 three times, including the new high reached on Friday.
Long-term borrowing costs also rose, with the yield on 30-year gilts climbing to 5.81%.
Borrowing costs for other governments also rose on Friday, as worries persist about how the Iran war could push up inflation due to the surge in energy costs.
The price of global oil benchmark Brent crude surged on Friday morning to over $109 a barrel, up from $105.72 on Thursday.
However, investors consider that a government led by Burnham would be more likely to increase Britain’s already high public borrowing.
In an interview with the New Statesman last year, Burnham said the government had to “get beyond this thing of being in hock to the bond markets”.
AJ Bell investment director Russ Mould said while there was no guarantee Burnham would win a seat in parliament or contest the leadership, his New Statesman comment had “helped push UK borrowing costs higher and seen the pound slump”.
“A process involving Burnham also promises to be more protracted and ‘noisy’, thereby prolonging and exacerbating the uncertainty about the political situation in the UK,” he said.