A report that the US President could name the new head of the central bank early raises concerns over its independence.
Economists have warned the rise could mean further tax hikes or spending cuts by the government.
Pound highest against dollar in a year as investors bet on UK rates staying higher for longer.
The stock index closes at a high as global inflation and interest rate fears ease.
Sterling has reached its highest level against the US dollar since mid-August.
The currency has rallied against the dollar in recent days, and rose further on Wednesday.
It comes as investors welcomed the appointment of Rishi Sunak and the dollar fell.
The pound has fallen against the dollar as the UK's financial and political turmoil continues.
Sterling initially rose sharply to $1.13 as investors reacted to the news of the prime minister's departure.
