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.