BBC reports investors have recently been unnerved by a string of bank failures.
But US stock markets were higher after Treasury Secretary Janet Yellen signalled the US government would protect people's deposits if another bank collapsed.
In the UK, the FTSE closed 1.79% higher after gains in top bank shares.
NatWest, Prudential and Barclays shares gained about 5%, while Standard Chartered and Lloyds also traded higher.
Ms Yellen said "the situation is stabilising, and the US banking system remains sound" in a speech on Tuesday.
This follows the collapse of Silicon Valley Bank and Signature Bank earlier this month.
The failures were triggered by depositors rushing to withdraw money after anxiety over the banks' health.
And last week, a group of the biggest US banks raised $30bn (£24.5bn) in funds for regional lender First Republic Bank, but its share price still crashed by more than 45% on Monday.
Ms Yellen said the US intervention in the two bank collapses was necessary to "protect the broader banking system", after promising that all depositors in both banks would be protected.
She added that similar action could be taken if the same happens to other smaller banks, indicating that savers would not lose their money if another bank were to collapse.
Photo Reuters Caption: Traders work on the floor of the New York Stock Exchange this week