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By Faisal Islam & Peter Hoskins
BBC News
The governor of the Bank of England says it is considering whether to raise the level of protection for savers.
Andrew Bailey's comments at the International Monetary Fund (IMF) meeting in Washington come after recent concerns over the banking system.
He also said reforms put in place after the global financial crisis had been effective during the recent turmoil.
In March, Silicon Valley Bank (SVB) and two other US lenders collapsed, and UBS was forced to buy rival Credit Suisse.
Mr Bailey has been generally positive about the world avoiding anything like the 2008 financial crisis.
However, he revealed here that the Bank is looking at upping levels of safety in the banking system, after the extraordinary experience of digital bank runs at SVB.
US authorities stepped in to protect deposits, whether or not they were insured. In the UK, SVB's British operation was sold to banking giant HSBC for a nominal £1.
Current bank safety rules assume a bank might only lose 20% of its deposit base over a month.
SVB UK lost a third of its deposits in just one day, amid social media rumours, with savers now able to instantly withdraw savings digitally.
The US Federal Reserve Chair called it the fastest bank run in American history.
The deposits of ordinary UK savers are currently protected up to £85,000 ($106,000) per saver per bank, that was itself greatly increased since the financial crisis, a decade and a half ago. In the US the figure stands at $250,000.
The EU and the US are considering raising their already higher levels of protection, but such moves would come at a cost to big banks, and potentially limit flows of credit.
The Chancellor, Jeremy Hunt, has also been meeting counterparts in Washington, agreeing new support for both for Ukraine, and developing countries hit by high interest rates on large pandemic debts.
Mr Bailey also said in Washington that "the post-crisis reforms to bank regulation have worked".
"Today I do not believe we face a systemic banking crisis," he added.
Concerns over the health of the global financial system triggered a slide in bank shares around the world, although markets have calmed in recent weeks.
It was seen by many commentators as the first major test of the more strict banking rules introduced in the wake of the global financial crisis more than a decade ago.