The pound rose against the dollar and government borrowing costs dipped as investors reacted to Prime Minister Liz Truss's resignation.
Sterling jumped to $1.13 at one point before slipping back, but was still higher than at the start of Thursday, reported BBC.
One analyst said the reaction suggested investors were "relieved" by the news, despite a lot of uncertainty remaining.
Business groups said the new prime minister would have to act quickly to restore confidence.
Government borrowing costs rose sharply last month after the government promised huge tax cuts in its mini-budget without saying how it would pay for them.
But these costs fell back after the Bank of England stepped in with an emergency support programme, and after Jeremy Hunt reversed nearly all the mini-budget measures when he became chancellor.
Mr Hunt is due to announce plans for spending and tax on 31 October in his economic plan, which the Treasury confirmed was set to go ahead.
"Although the resignation of Liz Truss as Prime Minister leaves the UK without a leader when it faces huge economic, fiscal and financial market challenges, the markets appear to be relieved," said Paul Dales, chief UK economist at Capital Economics.
He added that her resignation was "a step that needed to happen for the UK government to move further along the path towards restoring credibility in the eyes of the financial markets".
"But more needs to be done and the new prime minister and their chancellor have a big task to navigate the economy through the cost of living crisis, cost of borrowing crisis and the cost of credibility crisis."
Read: British pound hits record low against dollar
Simon French, chief economist at Panmure Gordon, said the market reaction had been "fairly muted", with investors waiting for the "detail of what comes next".
Ms Truss said her successor would be elected in a Tory leadership contest, to be completed in the next week. Her resignation came after a key minister quit and Tory MPs rebelled in a chaotic parliamentary vote on Wednesday.
Mr French said the markets could rally "more aggressively" if a clear favourite emerged for PM. "The sooner you get there the more likely the person who has won will have the support to do the difficult stuff."
The head of the CBI business lobby group, Tony Danker, said: "The politics of recent weeks have undermined the confidence of people, businesses, markets and global investors in Britain.
"Stability is key. The next prime minister will need to act to restore confidence from day one.
"They will need to deliver a credible fiscal plan for the medium term as soon as possible, and a plan for the long-term growth of our economy."
The interest rate - or yield - on UK government bonds for borrowing over a 10-year period climbed above 4% at one point on Thursday morning, but then fell back steadily as speculation grew about Ms Truss's possible departure.
Following the PM's statement, the rate edged higher again to about 3.8%, but still remained below the level seen at the start of the day.
Ahead of the PM's resignation, Bill Blain of Shard Capital had told the BBC that the markets had been "watching in a kind of stunned, open-mouthed horror" at political events.
"The problem we've got is that the last couple of weeks has really destroyed the image of political competency and that's one of the key elements to make any economy work," he said.